# Important Questions for Chapter 11 - Constructions

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Important questions based on NCERT syllabus for Chapter 11 - Constructions:

Question 1: Construct a Δ ABC in which AB = 4 cm, ∠ B = 60∘ and altitude CL = 3 cm. Construct a Δ ADE similar to Δ ABC such that each side of Δ ADE is 3/2 times that of the corresponding side of ΔABC
Solution: Steps of construction:

1. Construct a Δ ABC with given measurement
2. Extend AB to D such that AD = 32, AB = (32 × 4) cm = 6 cm
3. Draw DE∥BC, cutting AC produced at E.
4. Δ ADE is the required triangle similar to Δ ABC such that each side of Δ ADE is 32 times the corresponding side of Δ ABC

Question 2: Draw a circle of radius 5 cm. Take a point P on it. Without using the centre of the circle construct a tangent at the point P.
Solution: Steps of construction :

1. Draw a circle of radius 5 cm.
2. Mark a point P on it.
3. Draw any chord PQ.
4. Take a point R on the major arc QP.
5. Join PR and RQ.
6. Make ∠ QPT = ∠ PRQ [∵ Angles in the alternate segments are equal]
7. Produce TP to T', as shown in the figure.
8. T'PT is the required tangent at P.

Question 3: Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle.
Solution: Steps of construction :

1. Draw a circle with 'O' as centre and radius 7 cm.
2. Mark a point P outside the circle such that OP = 10cm.
3. Draw a line segment from P to the centre of the circle O and bisect it. Let it be at a point, say M.
4. With M as centre and PM as radius draw a circle. Let this circle intersect the initial circle at points X and Y
5. Join PX and PY and extend them to X' and Y' respectively.
6. PX' and PY' are the required tangents.
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