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Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
c0928203-206a-40ef-9d24-7decf59d6f4f
|
[
"images/c0928203-206a-40ef-9d24-7decf59d6f4f-0.png"
] | null | 1,737 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
3b376e47-7331-4659-bdcc-d1861847013a
|
[
"images/3b376e47-7331-4659-bdcc-d1861847013a-0.png"
] | null | 1,738 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
4bf46798-5a6e-4157-983f-0471ba10c446
|
[
"images/4bf46798-5a6e-4157-983f-0471ba10c446-0.png"
] | null | 1,739 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
15952f81-571e-482c-8f74-fd6c8d94c727
|
[
"images/15952f81-571e-482c-8f74-fd6c8d94c727-0.png"
] | null | 1,740 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
4d19173f-cfed-49b5-b320-0262fe02456e
|
[
"images/4d19173f-cfed-49b5-b320-0262fe02456e-0.png"
] | null | 1,741 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
92f2507a-c1e1-4ed0-8045-c9a7f7654ec6
|
[
"images/92f2507a-c1e1-4ed0-8045-c9a7f7654ec6-0.png"
] | null | 1,742 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
3223a645-bdac-48b7-9bf1-9b661ace46f3
|
[
"images/3223a645-bdac-48b7-9bf1-9b661ace46f3-0.png"
] | null | 1,743 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
aa9118e0-2fee-4993-968c-a80830556234
|
[
"images/aa9118e0-2fee-4993-968c-a80830556234-0.png"
] | null | 1,744 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
102164bf-2a9c-4d90-b932-c4a452f78626
|
[
"images/102164bf-2a9c-4d90-b932-c4a452f78626-0.png"
] | null | 1,745 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
1e236ea7-3775-4c76-80e3-83dd94977425
|
[
"images/1e236ea7-3775-4c76-80e3-83dd94977425-0.png"
] | null | 1,746 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
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|
[
"images/a3017a96-b2cc-4ec6-b882-52e99d82cd50-0.png"
] | null | 1,747 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
3fc68477-5118-46fc-a28e-b7b3b119a04d
|
[
"images/3fc68477-5118-46fc-a28e-b7b3b119a04d-0.png"
] | null | 1,748 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
30e93218-4d73-49f1-86be-65e4a9015f91
|
[
"images/30e93218-4d73-49f1-86be-65e4a9015f91-0.png"
] | null | 1,749 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
91349a3e-07a5-4274-b3d6-5f804df2a730
|
[
"images/91349a3e-07a5-4274-b3d6-5f804df2a730-0.png"
] | null | 1,750 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
d26301f3-5234-44e2-991b-7a050485252b
|
[
"images/d26301f3-5234-44e2-991b-7a050485252b-0.png"
] | null | 1,751 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
f3365cf1-3143-4aa3-ba8b-75cc113ff233
|
[
"images/f3365cf1-3143-4aa3-ba8b-75cc113ff233-0.png"
] | null | 1,752 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
90a90a3c-fc78-4123-a14f-1b96401d7bb1
|
[
"images/90a90a3c-fc78-4123-a14f-1b96401d7bb1-0.png"
] | null | 1,753 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
fc7845c0-4d3b-4a84-8c42-73d8c2a5f966
|
[
"images/fc7845c0-4d3b-4a84-8c42-73d8c2a5f966-0.png"
] | null | 1,754 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{A}"
] |
7796eebd-92f1-4243-9221-9800d2cf5ef7
|
[
"images/7796eebd-92f1-4243-9221-9800d2cf5ef7-0.png"
] | null | 1,755 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
a2ec2948-d807-4ab7-9b40-70c860e5b947
|
[
"images/a2ec2948-d807-4ab7-9b40-70c860e5b947-0.png"
] | null | 1,756 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
5a8272ac-8f5a-4229-9e8e-59957d4282be
|
[
"images/5a8272ac-8f5a-4229-9e8e-59957d4282be-0.png"
] | null | 1,757 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
2b3e5219-37bc-4fb4-85f6-fe53aad914c9
|
[
"images/2b3e5219-37bc-4fb4-85f6-fe53aad914c9-0.png"
] | null | 1,758 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
41cdb1fd-6a3c-47e7-a750-903b3bb0ea2a
|
[
"images/41cdb1fd-6a3c-47e7-a750-903b3bb0ea2a-0.png"
] | null | 1,759 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
c901a4e9-ca23-4abc-9171-9349bbe2ce8c
|
[
"images/c901a4e9-ca23-4abc-9171-9349bbe2ce8c-0.png"
] | null | 1,760 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
60183db5-c6a2-4076-b03e-8dc6662d3bc3
|
[
"images/60183db5-c6a2-4076-b03e-8dc6662d3bc3-0.png"
] | null | 1,761 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
88243d86-9f9c-4fd1-a024-1990841dde6c
|
[
"images/88243d86-9f9c-4fd1-a024-1990841dde6c-0.png"
] | null | 1,762 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
c5d3eaf3-3077-4b93-86ea-c68ae8dfa87e
|
[
"images/c5d3eaf3-3077-4b93-86ea-c68ae8dfa87e-0.png"
] | null | 1,763 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
dba72d86-e7fa-4918-acf0-f1871093fbcf
|
[
"images/dba72d86-e7fa-4918-acf0-f1871093fbcf-0.png"
] | null | 1,764 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
f55745c1-0511-4406-951d-de462533d455
|
[
"images/f55745c1-0511-4406-951d-de462533d455-0.png"
] | null | 1,765 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
4694763a-b974-472c-96d5-26b889ee6366
|
[
"images/4694763a-b974-472c-96d5-26b889ee6366-0.png"
] | null | 1,766 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
1bdc35e3-4a12-403c-825f-701e3f104d6a
|
[
"images/1bdc35e3-4a12-403c-825f-701e3f104d6a-0.png"
] | null | 1,767 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
959c37e6-d9a3-4ea7-9cf9-3c6a0b039c9e
|
[
"images/959c37e6-d9a3-4ea7-9cf9-3c6a0b039c9e-0.png"
] | null | 1,768 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
5bdea6e1-34c3-45f8-81c0-f0ea884c2db9
|
[
"images/5bdea6e1-34c3-45f8-81c0-f0ea884c2db9-0.png"
] | null | 1,769 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
2531e91c-6381-4726-bdfc-c917159b59f8
|
[
"images/2531e91c-6381-4726-bdfc-c917159b59f8-0.png"
] | null | 1,770 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
7846c85c-525d-4233-9c2e-74f16aa3c349
|
[
"images/7846c85c-525d-4233-9c2e-74f16aa3c349-0.png"
] | null | 1,771 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
6353621c-8334-4f1f-a4ee-e687a232185c
|
[
"images/6353621c-8334-4f1f-a4ee-e687a232185c-0.png"
] | null | 1,772 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
0d97732d-d137-47ab-a8a5-42964fd60298
|
[
"images/0d97732d-d137-47ab-a8a5-42964fd60298-0.png"
] | null | 1,773 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
ddd00257-ecf9-4762-a748-d659c1024411
|
[
"images/ddd00257-ecf9-4762-a748-d659c1024411-0.png"
] | null | 1,774 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
6ef16145-9107-406c-8122-628c62315716
|
[
"images/6ef16145-9107-406c-8122-628c62315716-0.png"
] | null | 1,775 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
6614adfb-7116-4e58-a978-bf0c49b4567c
|
[
"images/6614adfb-7116-4e58-a978-bf0c49b4567c-0.png"
] | null | 1,776 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
586148f5-01c8-4dce-9fc3-be9fb083d8dd
|
[
"images/586148f5-01c8-4dce-9fc3-be9fb083d8dd-0.png"
] | null | 1,777 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
a7c5cbd1-6a18-4229-8a16-f10b246d5446
|
[
"images/a7c5cbd1-6a18-4229-8a16-f10b246d5446-0.png"
] | null | 1,778 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
3af3e0de-99a4-4504-963f-1fdbf522e645
|
[
"images/3af3e0de-99a4-4504-963f-1fdbf522e645-0.png"
] | null | 1,779 |
Question: From the four options given, choose the most appropriate one to fill in the question mark so that it shows a certain regularity:
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{B}"
] |
85eb4cd7-d95c-490a-9422-9ea5126c068c
|
[
"images/85eb4cd7-d95c-490a-9422-9ea5126c068c-0.png"
] | null | 1,780 |
Question: The picture on the left shows a cuboid made up of 8 white cubes and 4 black cubes glued together. Which of the following cannot be the unfolded view of its outer surface?
Choices:
A. A B. B C. C D. D
|
[
"\\boxed{D}"
] |
25b56e9c-fdd6-4739-8aa3-173d186b88f2
|
[
"images/25b56e9c-fdd6-4739-8aa3-173d186b88f2-0.png"
] | null | 1,781 |
As shown in the figure, in $\triangle ABC$, $\angle BAC=130^\circ$, the perpendicular bisectors of $AB$ and $AC$ intersect $BC$ at points $E$ and $F$, and intersect $AB$ and $AC$ at points $D$ and $G$, respectively. What is the measure of $\angle EAF$?
|
[
"\\boxed{80}"
] |
834fb22b-6092-4705-93b3-fe7b803b3a70
|
[
"images/834fb22b-6092-4705-93b3-fe7b803b3a70-0.png"
] | null | 1,782 |
As shown in the figure, in $ \triangle ABC$, EF is the perpendicular bisector of AB, intersecting AB at point D. If BF = 6 and CF = 2, then what is the length of AC?
|
[
"\\boxed{8}"
] |
09a3fd37-6665-4076-871d-d8ff5739576b
|
[
"images/09a3fd37-6665-4076-871d-d8ff5739576b-0.png"
] | null | 1,783 |
As shown in the figure, in $\triangle ABC$, $\angle ACB=90^\circ$, $AC=5$, $BC=12$. Rotating $\triangle ABC$ $60^\circ$ clockwise around point $B$ results in $\triangle BDE$. When $DC$ is connected and intersects $AB$ at point $F$, what is the sum of the perimeters of $\triangle ACF$ and $\triangle BDF$?
|
[
"\\boxed{42}"
] |
8ba13f9e-f8b7-4a22-9a46-4a9022ee46c5
|
[
"images/8ba13f9e-f8b7-4a22-9a46-4a9022ee46c5-0.png"
] | null | 1,784 |
As shown in the figure, in quadrilateral ABCD, connect AC and BD. If $\triangle ABC$ is an equilateral triangle, with $AB=BD$ and $\angle ABD=20^\circ$, then what is the measure of $\angle BDC$?
|
[
"\\boxed{70}"
] |
7ccd5f7b-1be1-4326-b13c-6352d078929e
|
[
"images/7ccd5f7b-1be1-4326-b13c-6352d078929e-0.png"
] | null | 1,785 |
As shown in the figure, in quadrilateral $ABCD$, $E$ is the midpoint of $AB$, and $EC$ intersects $BD$ at point $F$. What is the ratio of the area of $\triangle BEF$ to the area of $\triangle BCF$?
|
[
"\\boxed{1:2}"
] |
22977fb9-c2fb-44f2-b836-9d4eb51cc3dd
|
[
"images/22977fb9-c2fb-44f2-b836-9d4eb51cc3dd-0.png"
] | null | 1,786 |
As shown in the diagram, square ABCD and square EFOG are similar figures, where point A corresponds to point E. The coordinate of point A is $(-4, 2)$, and the coordinate of point E is $(-1, 1)$. What are the coordinates of the center of similitude of these two squares?
|
[
"\\boxed{(2,0)}"
] |
0348dddc-c402-43b7-94cc-e81f45c5d04f
|
[
"images/0348dddc-c402-43b7-94cc-e81f45c5d04f-0.png"
] | null | 1,787 |
As shown in the figure, in $\triangle ABC$, points $D, E, F$ are on the sides $AB$, $AC$, and $BC$ respectively, with $DE \parallel BC$, $EF \parallel AB$, and $AD: DB = 3:5$, what is the ratio of $BF: CF$?
|
[
"\\boxed{\\frac{3}{5}}"
] |
0a5f324c-fb52-48fb-a9d5-f74c779fe4dc
|
[
"images/0a5f324c-fb52-48fb-a9d5-f74c779fe4dc-0.png"
] | null | 1,788 |
As shown in the figure, in rectangle $ABCD$, $AB=8$. The rectangle is folded along the line $AC$, with point $B$ falling onto point $E$, and $AE$ intersects $CD$ at point $F$. If $AF=\frac{25}{4}$, what is the length of $AD$?
|
[
"\\boxed{6}"
] |
a4692541-8e4e-470e-b984-3f2d40b32c53
|
[
"images/a4692541-8e4e-470e-b984-3f2d40b32c53-0.png"
] | null | 1,789 |
As shown in the figure, diagonals AC and BD of rhombus ABCD intersect at point O. A perpendicular line is drawn from point C to the extended line of AB, intersecting it at point E. Line OE is then drawn. If AB = $2\sqrt{5}$ and BD = 4, what is the length of OE?
|
[
"\\boxed{4}"
] |
9a2d787c-0818-486d-bce2-61b0f18cbff1
|
[
"images/9a2d787c-0818-486d-bce2-61b0f18cbff1-0.png"
] | null | 1,790 |
As shown in the figure, in $\triangle ABC$, $\angle B=\angle C$, $D$ is a point on side $BC$, and $E$ is a point on side $AC$, with $\angle ADE=\angle AED$. If $\angle BAD=28^\circ$, what is the measure of $\angle CDE$?
|
[
"\\boxed{14}"
] |
f28e27e9-694e-45d5-b09b-c054469e5304
|
[
"images/f28e27e9-694e-45d5-b09b-c054469e5304-0.png"
] | null | 1,791 |
As shown in the figure, in $\triangle ABC$, $AB=AC=13$ and $BC=10$, what is the value of $\sin B$?
|
[
"\\boxed{\\frac{12}{13}}"
] |
fd96748e-7629-4a5f-8f29-21f534bc1bc4
|
[
"images/fd96748e-7629-4a5f-8f29-21f534bc1bc4-0.png"
] | null | 1,792 |
In the coordinate system shown, let $O(0,0)$, $A(3,3\sqrt{3})$, and $B(6,0)$. If $\triangle OAB$ is folded along line $CD$ such that point $A$ precisely falls on point $E$ on segment $OB$ and given that $OE=\frac{6}{5}$, what is the value of $AC: AD$?
|
[
"\\boxed{\\frac{2}{3}}"
] |
63b538c1-374b-4ad3-af38-5ee273409302
|
[
"images/63b538c1-374b-4ad3-af38-5ee273409302-0.png"
] | null | 1,793 |
As shown in the figure, AB is the diameter of $\odot O$, CD is a chord of $\odot O$, $\angle CAB=55^\circ$, then what is the degree measure of $\angle D$?
|
[
"\\boxed{35}"
] |
57f92733-4db4-4b45-a052-b8a9fb6933dd
|
[
"images/57f92733-4db4-4b45-a052-b8a9fb6933dd-0.png"
] | null | 1,794 |
In the diagram, within $\triangle ABC$, $\angle A=90^\circ$, $AB=8$, $AC=6$, point $D$ is a moving point on $BC$. Lines are drawn from $D$ such that $DE\perp AB$ and $DF\perp AC$, with $E$ and $F$ being the feet of the perpendiculars, respectively. What is the minimum value of $EF$?
|
[
"\\boxed{4.8}"
] |
02705f88-d244-44c8-9fbe-02591a932fc3
|
[
"images/02705f88-d244-44c8-9fbe-02591a932fc3-0.png"
] | null | 1,795 |
As shown in the figure, the diagonals of square $ABCD$ intersect at point $O$. $E$ is any point on $BC$, $EG \perp BD$ at point $G$, and $EF \perp AC$ at point $F$. If $AC=10$, what is the value of $EG+EF$?
|
[
"\\boxed{5}"
] |
5bde9201-a3ae-4d7f-b79f-bbd4dce3acca
|
[
"images/5bde9201-a3ae-4d7f-b79f-bbd4dce3acca-0.png"
] | null | 1,796 |
As shown in the figure, in circle $\odot O$, C and D are two points on circle $\odot O$, and AB is the diameter of $\odot O$. Given that $\angle AOC = 130^\circ$, what is the measure of $\angle BDC$?
|
[
"\\boxed{25}"
] |
9e2ae98e-a3e0-46f5-8880-7bcb5514fdba
|
[
"images/9e2ae98e-a3e0-46f5-8880-7bcb5514fdba-0.png"
] | null | 1,797 |
As shown in the figure, points $A$, $B$, $C$, $D$ are all on the circle $\odot O$, $\angle BAC=15^\circ$, $\angle BOD=70^\circ$, and $DE$ is tangent to $\odot O$ at $D$. What is the measure of $\angle CDE$?
|
[
"\\boxed{20}"
] |
3f48e589-8c91-432e-91a4-eb8f02b490a3
|
[
"images/3f48e589-8c91-432e-91a4-eb8f02b490a3-0.png"
] | null | 1,798 |
As shown in the figure, in $\triangle ABC$, $AB = AC$, $EF$ is the perpendicular bisector of $AC$, intersecting $AC$ at point $E$ and $AB$ at point $F$. $D$ is the midpoint of side $BC$, and $M$ is a moving point on segment $EF$. If $BC = 4$ and the area of $\triangle ABC$ is 16, what is the minimum perimeter of $\triangle CDM$?
|
[
"\\boxed{10}"
] |
11353fa1-d312-44ba-885d-2f81240a4bcd
|
[
"images/11353fa1-d312-44ba-885d-2f81240a4bcd-0.png"
] | null | 1,799 |
As shown in the figure, the musical staff is composed of five equidistant and equal-length parallel horizontal lines. There are three points, A, B, and C, all located on the lines. If the length of segment AB equals \( \frac{3}{2} \), what is the length of segment BC?
|
[
"\\boxed{\\frac{3}{4}}"
] |
16ce4cb2-6c23-4b98-8d31-43d913ad6e36
|
[
"images/16ce4cb2-6c23-4b98-8d31-43d913ad6e36-0.png"
] | null | 1,800 |
As shown in the figure, point \(O\) is a point inside \(\triangle ABC\), \(\angle ABO=30^\circ\), \(\angle ACO=15^\circ\), \(\angle BOC=100^\circ\), then what is the degree measure of \(\angle A\)?
|
[
"\\boxed{55}"
] |
e93f118e-6618-4312-bd36-3d6f7465214d
|
[
"images/e93f118e-6618-4312-bd36-3d6f7465214d-0.png"
] | null | 1,801 |
As shown in the figure, the area of $\triangle ABC$ is 24. Point $D$ is a point on side $AC$, and extending $BD$ intersects the line parallel to $BC$ through point $A$ at point $E$. Connect $EC$, and construct parallelogram $DECF$ with $DE$ and $EC$ as adjacent sides. $DF$ intersects side $BC$ at point $H$. Connect $AH$. When $AD = \frac{1}{2}CD$, what is the area of $\triangle AHC$?
|
[
"\\boxed{8}"
] |
096b5d84-e102-4baa-a9dc-87d0fd1efee9
|
[
"images/096b5d84-e102-4baa-a9dc-87d0fd1efee9-0.png"
] | null | 1,802 |
In the figure, within $\triangle ABC$, $CD\perp AB$ at point $D$, and $E$, $F$ are the midpoints of $AC$, $BC$, respectively. Given $AB=10$, $BC=8$, and $DE=4.5$, what is the perimeter of $\triangle DEF$?
|
[
"\\boxed{13.5}"
] |
5e8ea058-afd2-4a1a-9b89-058c993defd4
|
[
"images/5e8ea058-afd2-4a1a-9b89-058c993defd4-0.png"
] | null | 1,803 |
As shown in the figure, quadrilateral $ABCD$ is a kite, with diagonals $AC$ and $BD$ intersecting at point $O$, and $DH \perp AB$ at point $H$. Connect $OH$, and $\angle CAD=25^\circ$. What is the measure of $\angle DHO$?
|
[
"\\boxed{25}"
] |
2d451d68-c762-4bbc-8c66-179d9023e78d
|
[
"images/2d451d68-c762-4bbc-8c66-179d9023e78d-0.png"
] | null | 1,804 |
As illustrated in the diagram, within rectangle ABCD, point E is the midpoint of BC. Line AE intersects BD at point F. If $BF = 2$, what is the length of BD?
|
[
"\\boxed{6}"
] |
f9004988-fc27-48cd-9fca-da51eccea72a
|
[
"images/f9004988-fc27-48cd-9fca-da51eccea72a-0.png"
] | null | 1,805 |
As shown in the figure, in $\triangle ABC$, $\angle BAD = \angle CAD$, $BE = CE$, $AD \perp BD$, $DE = \frac{3}{2}$, $AB = 4$, what is the value of $AC$?
|
[
"\\boxed{7}"
] |
f3c754a3-26ca-4cae-88c2-39a23a0f2d4a
|
[
"images/f3c754a3-26ca-4cae-88c2-39a23a0f2d4a-0.png"
] | null | 1,806 |
As shown in the figure, in $\triangle ABC$, $D$, $E$, and $F$ are the midpoints of sides $BC$, $CA$, and $AB$, respectively. What is the perimeter of the quadrilateral $AFDE$?
|
[
"\\boxed{AB + AC}"
] |
54a1a5b8-6332-4b53-81a8-bf6ec3e9de4b
|
[
"images/54a1a5b8-6332-4b53-81a8-bf6ec3e9de4b-0.png"
] | null | 1,807 |
As shown in the figure, in $ \triangle ABC$, $ AC=2$, $ BC=4$, and D is a point on BC, $ \angle CAD=\angle B$, the area of $ \triangle ADC$ is $a$, then what is the area of $ \triangle ABD$?
|
[
"\\boxed{3a}"
] |
27edd8a4-ee94-4fa4-9738-db25b5819dcf
|
[
"images/27edd8a4-ee94-4fa4-9738-db25b5819dcf-0.png"
] | null | 1,808 |
As shown in the figure, in quadrilateral $ABCD$, point $E$ is the midpoint of side $AD$, and $EC$ intersects the diagonal $BD$ at point $F$. If the area of $\triangle DEF$ is $3$, what is the area of quadrilateral $ABCD$?
|
[
"\\boxed{36}"
] |
4c93a25a-68d7-4dfa-82bd-17e92e596041
|
[
"images/4c93a25a-68d7-4dfa-82bd-17e92e596041-0.png"
] | null | 1,809 |
The squares $A_1B_1C_1O$, $A_2B_2C_2C_1$, $A_3B_3C_3C_2$, … are placed as shown in the figure, where points $A_1, A_2, A_3, $… and points $C_1, C_2, C_3, $… are on the line $y=x+1$ and the x-axis, respectively. What is the y-coordinate of point $B_{2022}$?
|
[
"\\boxed{2^{2021}}"
] |
491738d2-ffdd-4943-97c0-c318ede268a7
|
[
"images/491738d2-ffdd-4943-97c0-c318ede268a7-0.png"
] | null | 1,810 |
The diagram shows a schematic of an arched bridge, with the points where the arch intersects the deck being O and B, respectively. Taking point O as the origin and the horizontal line OB as the x-axis, we establish a Cartesian coordinate system. The arch of the bridge can be approximated by the parabola $y=-0.01(x-20)^2+4$. The point C, where the arch intersects the pier AC, is precisely at the water's surface, and $AC \perp x$-axis. If OA is 5 meters, what is the height of the deck above the water surface AC?
|
[
"\\boxed{2.25}"
] |
ab746e9d-0c04-4ac2-bead-78f9bcae3cc7
|
[
"images/ab746e9d-0c04-4ac2-bead-78f9bcae3cc7-0.png"
] | null | 1,811 |
As shown in the figure, AB is the diameter of $\odot O$. Point D is on the extension line of AB, and DC is tangent to $\odot O$ at point C. If $\angle A = 20^\circ$, what is the measure of $\angle D$?
|
[
"\\boxed{50}"
] |
7cff4adc-9d29-41fe-8ae6-613e45dfe70a
|
[
"images/7cff4adc-9d29-41fe-8ae6-613e45dfe70a-0.png"
] | null | 1,812 |
As illustrated, $E$ is a point within $\triangle ABC$, $BE$ bisects $\angle ABC$, $AD \perp BE$ at point $E$, intersecting $BC$ at point $D$, where point $D$ is precisely on the perpendicular bisector of side $AC$, $BC=10$, and $AB=6$. What is the length of $AE$?
|
[
"\\boxed{2}"
] |
d3c781cf-71a3-4999-aaec-9e7c89f91b7a
|
[
"images/d3c781cf-71a3-4999-aaec-9e7c89f91b7a-0.png"
] | null | 1,813 |
As shown in the figure, in $\triangle ABC$, $\angle B=90^\circ$, arcs are drawn with centers at $A$ and $C$ and radii greater than the length of $AC$, intersecting at points $M$ and $N$. Line $MN$ is drawn, intersecting $AC$ and $BC$ at $D$ and $E$ respectively. Connect $AE$. If $AB=6$ and $AC=10$, what is the perimeter of $\triangle ABE$?
|
[
"\\boxed{14}"
] |
f7d8ef82-41be-467a-8d2a-0c68085cc5f2
|
[
"images/f7d8ef82-41be-467a-8d2a-0c68085cc5f2-0.png"
] | null | 1,814 |
As shown in the figure, $ \angle B=35^\circ$, and $CD$ is the perpendicular bisector of $AB$, then what is the value of $ \angle ACE$?
|
[
"\\boxed{70}"
] |
f2fa61aa-3d61-4252-b1ce-85ad1d23fed9
|
[
"images/f2fa61aa-3d61-4252-b1ce-85ad1d23fed9-0.png"
] | null | 1,815 |
As shown in the figure, the line $y=x+b$ intersects with the line $y=kx+6$ at the point $P(1,3)$. What is the solution set for the inequality $x+b>kx+6$ with respect to $x$?
|
[
"\\boxed{x>1}"
] |
b40283d8-f20b-46c1-9611-713d761c0f9f
|
[
"images/b40283d8-f20b-46c1-9611-713d761c0f9f-0.png"
] | null | 1,816 |
As shown in the figure, the medians $AD$ and $BE$ of $\triangle ABC$ intersect each other at point $F$. Through point $E$, draw $EG\parallel AD$ where it intersects $BC$ at point $G$. What is the value of the ratio $EG\colon AF$?
|
[
"\\boxed{\\frac{3}{4}}"
] |
89fcd14a-8df8-48db-b46f-e4db6ca77b33
|
[
"images/89fcd14a-8df8-48db-b46f-e4db6ca77b33-0.png"
] | null | 1,817 |
As shown in the figure, the quadrilateral $ABCD$ is an inscribed quadrilateral of the circle, with $AB$ as the diameter. It is given that $\overset{\frown}{DC} = \overset{\frown}{CB}$, and if $\angle DCB = 110^\circ$, what is the degree measure of $\angle ABC$?
|
[
"\\boxed{55}"
] |
f052151a-29bf-4cc5-a472-714a0580fdd4
|
[
"images/f052151a-29bf-4cc5-a472-714a0580fdd4-0.png"
] | null | 1,818 |
As shown in the figure, with $O$ in the center, point $C$ is on the arc $\overset{\frown}{AB}$, and $\angle ADC$, $\angle BEC$ are the angles subtended by arcs $\overset{\frown}{AC}$, $\overset{\frown}{BC}$ on the circumference, respectively. If $\angle AOB=110^\circ$ and $\angle ADC=20^\circ$, what is the measure of $\angle BEC$?
|
[
"\\boxed{35}"
] |
388bae02-ca2a-4e07-9c06-22d00e0575ae
|
[
"images/388bae02-ca2a-4e07-9c06-22d00e0575ae-0.png"
] | null | 1,819 |
As shown in the figure, a right-angled triangle ruler with an angle of $45^\circ$ is placed on two parallel lines $m$ and $n$. If $\angle \alpha = 118^\circ$, then what is the degree measure of $\angle \beta$?
|
[
"\\boxed{73}"
] |
e287702d-1e3c-4cca-b73b-504a03c84d49
|
[
"images/e287702d-1e3c-4cca-b73b-504a03c84d49-0.png"
] | null | 1,820 |
As shown in the figure, in $\triangle ABC$, $\angle C=90^\circ$, $\angle BAC=70^\circ$. The triangle $\triangle ABC$ is rotated $70^\circ$ clockwise around point A, with the corresponding points of B and C after rotation being B' and C', respectively. Connecting BB', what is the degree measure of $\angle BB'C'$?
|
[
"\\boxed{35}"
] |
d1918304-733f-4062-859a-b3db0f48d325
|
[
"images/d1918304-733f-4062-859a-b3db0f48d325-0.png"
] | null | 1,821 |
As shown in the figure, $AB\parallel CD\parallel EF$, if $BF=3DF$, then what is the value of $\frac{AC}{CE}$?
|
[
"\\boxed{2}"
] |
011db40a-d4b6-422c-b3fc-492a78295931
|
[
"images/011db40a-d4b6-422c-b3fc-492a78295931-0.png"
] | null | 1,822 |
As illustrated, $\triangle PAC \cong \triangle PBD$, given that $\angle A=40^\circ$ and $\angle BPD=20^\circ$, what is the measure of $\angle PCD$?
|
[
"\\boxed{60}"
] |
a926e6ef-dfeb-48e6-a2c2-4db14f2678e0
|
[
"images/a926e6ef-dfeb-48e6-a2c2-4db14f2678e0-0.png"
] | null | 1,823 |
As shown in the diagram, it is known that $\angle MON=30^\circ$, points $A_1$, $A_2$, $A_3$, ... are on ray $ON$, and points $B_1$, $B_2$, $B_3$, ... are on ray $OM$. The triangles $\triangle A_1B_1A_2$, $\triangle A_2B_2A_3$, $\triangle A_3B_3A_4$, ... are all equilateral triangles. If $OA_1=3$, what is the side length of $\triangle A_{10}B_{10}A_{11}$?
|
[
"\\boxed{1536}"
] |
4e0cefdd-8235-46a4-9b4f-76a8d4c4bb2b
|
[
"images/4e0cefdd-8235-46a4-9b4f-76a8d4c4bb2b-0.png"
] | null | 1,824 |
As shown in the figure, point $P$ is a point inside $\angle AOB$. The symmetric point of $P$ with respect to $OA$ is $C$, and the symmetric point of $P$ with respect to $OB$ is $D$. Connect $CD$ intersecting $OA$, $OB$ at points $M$ and $N$ respectively, and then connect $PM$, $PN$. If $\angle AOB=50^\circ$, what is the measure of $\angle MPN$ in degrees?
|
[
"\\boxed{80}"
] |
6f128dba-9c8c-4773-b261-6b8b3797f3eb
|
[
"images/6f128dba-9c8c-4773-b261-6b8b3797f3eb-0.png"
] | null | 1,825 |
As shown in the figure, the line $y=kx+b$ passes through point $A(-1, -3)$ and point $B(-2, 0)$, and the line $y=3x$ passes through point $A$. What is the solution set of the inequality $3x<kx+b<0$?
|
[
"\\boxed{-2<x<-1}"
] |
01909912-e8a7-45fb-8827-41b07cb05fd2
|
[
"images/01909912-e8a7-45fb-8827-41b07cb05fd2-0.png"
] | null | 1,826 |
As shown in the figure, the line $y_1=x+b$ intersects with $y_2=kx-1$ at point P. What is the solution set of the inequality $x+b>kx-1$ with respect to $x$?
|
[
"\\boxed{x > -1}"
] |
fc3f89b9-c855-4103-b1b6-fd6993822de9
|
[
"images/fc3f89b9-c855-4103-b1b6-fd6993822de9-0.png"
] | null | 1,827 |
As shown in the figure, $AB \parallel EF$, $\angle ABC = 75^\circ$, $\angle CDF = 135^\circ$. What is the measure of $\angle BCD$ in degrees?
|
[
"\\boxed{30}"
] |
92edecbb-ffaa-4281-bcf1-6f3379ab81e4
|
[
"images/92edecbb-ffaa-4281-bcf1-6f3379ab81e4-0.png"
] | null | 1,828 |
As shown in the figure, $DE$ is the perpendicular bisector of side $AC$ of $\triangle ABC$, with the foot of the perpendicular at point $E$, intersecting $AB$ at point $D$. Connect $CD$, $\angle B=30^\circ$, $CD\perp BC$, $CD=3$, then what is the length of $AB$?
|
[
"\\boxed{9}"
] |
b634630e-e57a-420f-a6d4-95d424ec9269
|
[
"images/b634630e-e57a-420f-a6d4-95d424ec9269-0.png"
] | null | 1,829 |
As shown in the diagram, in rectangle $ABCD$, points $E$ and $F$ are located on sides $BC$ and $AD$ respectively. The rectangle is folded along $EF$ such that point $B$ falls exactly on point $H$ on side $AD$. Given that the area of rectangle $ABCD$ is $16\sqrt{3}$ and $FH = 2HD$, what is the length of the crease $EF$?
|
[
"\\boxed{4}"
] |
e326a7a6-4dd1-4cff-a69e-ec5ce2cdf65c
|
[
"images/e326a7a6-4dd1-4cff-a69e-ec5ce2cdf65c-0.png"
] | null | 1,830 |
As shown in the figure, within a $5\times4$ square grid, where each small square has a side length of $1$, the vertices of $\triangle ABC$ are all located at the vertices of these small squares. What is the value of $\tan\angle ABC$?
|
[
"\\boxed{4}"
] |
091ac8d5-33ea-429f-9dbb-e9a444e52b63
|
[
"images/091ac8d5-33ea-429f-9dbb-e9a444e52b63-0.png"
] | null | 1,831 |
In the figure, in the equilateral triangle $ABC$ with a side length of $2\sqrt{3}$, the moving points $D$ and $E$ are on the sides $BC$ and $AC$, respectively, maintaining $AE=CD$. Lines $BE$ and $AD$ are drawn and intersect at point $P$. What is the minimum value of $CP$?
|
[
"\\boxed{2}"
] |
40da3d9c-e940-44bf-85aa-afcb798c8d46
|
[
"images/40da3d9c-e940-44bf-85aa-afcb798c8d46-0.png"
] | null | 1,832 |
As shown in the figure, in the Cartesian coordinate system $xOy$, where $O$ is the origin, point $B$ is on the positive half-axis of the x-axis, and quadrilateral $OBCA$ is a parallelogram. It is given that $\sin\angle AOB=\frac{4}{5}$. The inverse proportion function $y=\frac{m}{x}$ ($m>0$) passes through point $A$ in the first quadrant and intersects $BC$ at point $F$. If point $F$ is the midpoint of $BC$, and the area of $\triangle AOF$ is 12, then what is the value of $m$?
|
[
"\\boxed{16}"
] |
c750fc5b-24d4-48da-adf8-650a6f290730
|
[
"images/c750fc5b-24d4-48da-adf8-650a6f290730-0.png"
] | null | 1,833 |
As shown in the figure, the grid is a square grid, and points A, B, C are the intersections of the grid lines. Let $\angle BAC = \alpha$, then what is $\tan\alpha$?
|
[
"\\boxed{\\frac{1}{3}}"
] |
ff244618-a3e7-4b2d-a356-119c007970f6
|
[
"images/ff244618-a3e7-4b2d-a356-119c007970f6-0.png"
] | null | 1,834 |
The shapes conforming to the golden ratio \( \left(\frac{\sqrt{5}-1}{2}\right) \) are often visually pleasing. In the pentagram shown, where \( AD=BC=\frac{\sqrt{5}+1}{2} \), and both points C and D are the golden sections of \( AB \), what is the length of \( CD \)?
|
[
"\\boxed{1}"
] |
008f8f75-e991-47b1-adfd-e2862a6b8d5d
|
[
"images/008f8f75-e991-47b1-adfd-e2862a6b8d5d-0.png"
] | null | 1,835 |
As shown in the figure, in $\triangle ABC$, $\angle ACB=90^\circ$, two squares are constructed externally on the sides AC and AB of $\triangle ABC$, denoted as $S_1$ and $S_2$ representing the areas of these two squares respectively. If $S_1=8$ and $S_2=17$, what is the length of BC?
|
[
"\\boxed{3}"
] |
ced965a4-de8c-49d0-b935-a81756ed0bcd
|
[
"images/ced965a4-de8c-49d0-b935-a81756ed0bcd-0.png"
] | null | 1,836 |
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