My Math Forum Rectangle inscribed in a circle

 Geometry Geometry Math Forum

 February 18th, 2019, 11:13 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory Rectangle inscribed in a circle Is the area of a rectangle inscribed in a circle ever rational?
 February 18th, 2019, 11:41 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402 put a $1 \times 1$ square inside a circle with radius $\dfrac{1}{\sqrt{2}}$ is one of infinite examples.
 February 19th, 2019, 02:17 AM #3 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory Other than a square?
 February 19th, 2019, 02:21 AM #4 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory Mea culpa. You're right, romsek.
 February 19th, 2019, 04:42 AM #5 Senior Member   Joined: Sep 2016 From: USA Posts: 645 Thanks: 408 Math Focus: Dynamical systems, analytic function theory, numerics Take any rectangle with rational area. Circumscribe it by a circle. This is always possible since rectangles are cyclic quadrilaterals. Thanks from Loren
February 19th, 2019, 08:12 AM   #6
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,552
Thanks: 1402

Quote:
 Originally Posted by Loren Other than a square?
SDK has answered this but it should be clear that because the distance from the center of a rectangle to each of the corners is a constant that any rectangle can be inscribed in a circle.

 Tags circle, inscribed, rectangle

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post SafetySkull Math 3 January 23rd, 2016 01:49 PM matisolla Geometry 1 May 26th, 2015 09:09 AM HawkI Math 0 March 30th, 2015 03:08 PM Hiks7888 Geometry 4 May 20th, 2014 09:28 PM tiba Algebra 3 June 20th, 2012 05:56 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49413779377937317, "perplexity": 8155.252120534818}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573735.34/warc/CC-MAIN-20190919204548-20190919230548-00063.warc.gz"}