{"id":102,"date":"2022-04-25T16:54:44","date_gmt":"2022-04-25T16:54:44","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=102"},"modified":"2022-04-25T16:55:49","modified_gmt":"2022-04-25T16:55:49","slug":"solve-two-equal-rectangles-in-a-circle","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/04\/25\/solve-two-equal-rectangles-in-a-circle\/","title":{"rendered":"Solve Two Equal Rectangles in a Circle"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"883\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-03-simple-1024x883.png\" alt=\"\" class=\"wp-image-103\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-03-simple-1024x883.png 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-03-simple-300x259.png 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-03-simple-768x663.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-03-simple-1536x1325.png 1536w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-03-simple-2048x1767.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Here is a new geometry problem with two equal rectangles in a circle that you might like to try. The corner of one rectangle touches the midpoint of a side of the other. The left hand rectangle is horizontal in the diagram and the right hand rectangle is tilted 30 degrees from vertical. I created this construction using Geogebra. Ed Staples, who I collaborate with on this series of problems, made the following labelled diagram. Can you find the width <em>2a<\/em> of the rectangles in terms of their height <em>h<\/em>, and the radius of the circle when <em>h<\/em> is 1?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"919\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-Ed-Staples-version-1024x919.jpeg\" alt=\"\" class=\"wp-image-105\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-Ed-Staples-version-1024x919.jpeg 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-Ed-Staples-version-300x269.jpeg 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-Ed-Staples-version-768x689.jpeg 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/equal-rectangles-in-circle-Ed-Staples-version.jpeg 1042w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Here is a new geometry problem with two equal rectangles in a circle that you might like to try. The corner of one rectangle touches the&#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-102","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/102","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=102"}],"version-history":[{"count":1,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/102\/revisions"}],"predecessor-version":[{"id":106,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/102\/revisions\/106"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}