{"id":107,"date":"2022-05-02T20:31:36","date_gmt":"2022-05-02T20:31:36","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=107"},"modified":"2022-05-02T20:35:08","modified_gmt":"2022-05-02T20:35:08","slug":"two-equal-rectangles-in-a-circle-solved","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/05\/02\/two-equal-rectangles-in-a-circle-solved\/","title":{"rendered":"Two Equal Rectangles in a Circle Solved"},"content":{"rendered":"\n<p>In my previous post I presented a geometry problem with two equal rectangles in a circle. <a href=\"https:\/\/convexabacus.xyz\/index.php\/2022\/04\/25\/solve-two-equal-rectangles-in-a-circle\/\">https:\/\/convexabacus.xyz\/index.php\/2022\/04\/25\/solve-two-equal-rectangles-in-a-circle\/<\/a><\/p>\n\n\n\n<p>I am happy to report that it was solved by Ed Staples. His solution is shown below, applying the cosine rule on triangle OST, not QTB, which is a typo in the image. Given that the height of the rectangle is 1, he calculates that the width (2a) of the rectangle is sqrt(3)\/6 and the radius of the circle is (sqrt(7\/3))\/2. <\/p>\n\n\n\n<p>There is more than one way to approach this problem. It was solved independently by three members of LinkedIn when Ed posted the problem there. If you don&#8217;t know where to start, I suggest looking for 30-60-90 degree triangles in the construction.<\/p>\n\n\n\n<p>I created this construction by exploring several variations using Geogebra and this was the only one I could find that led to a good mathematics problem. A simpler way of fitting two equal rectangles in a circle is left as an exercise for the reader.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"722\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/05\/equal-rectangles-in-circle-Ed-Staples-solution-1024x722.jpeg\" alt=\"\" class=\"wp-image-108\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/05\/equal-rectangles-in-circle-Ed-Staples-solution-1024x722.jpeg 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/05\/equal-rectangles-in-circle-Ed-Staples-solution-300x211.jpeg 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/05\/equal-rectangles-in-circle-Ed-Staples-solution-768x541.jpeg 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/05\/equal-rectangles-in-circle-Ed-Staples-solution.jpeg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In my previous post I presented a geometry problem with two equal rectangles in a circle. https:\/\/convexabacus.xyz\/index.php\/2022\/04\/25\/solve-two-equal-rectangles-in-a-circle\/ I am happy to report that it was solved&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-107","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/107","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=107"}],"version-history":[{"count":2,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/107\/revisions"}],"predecessor-version":[{"id":111,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/107\/revisions\/111"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}