{"id":3404,"date":"2023-12-16T12:28:25","date_gmt":"2023-12-16T17:28:25","guid":{"rendered":"https:\/\/josmfs.net\/?p=3404"},"modified":"2023-12-16T12:28:25","modified_gmt":"2023-12-16T17:28:25","slug":"more-right-triangle-magic","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/12\/16\/more-right-triangle-magic\/","title":{"rendered":"More Right Triangle Magic"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3402\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/12\/More-Right-Triangle-Magic-Fig2.jpg\" alt=\"\" width=\"200\" height=\"245\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/12\/More-Right-Triangle-Magic-Fig2.jpg 403w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/12\/More-Right-Triangle-Magic-Fig2-245x300.jpg 245w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/p>\n<p><a href=\"https:\/\/twitter.com\/jamestanton\/status\/1536299591183867906.\">James Tanton<\/a> asked to prove the following surprising property of a right triangle and its circumscribed and inscribed circles.<\/p>\n<p>\u201cEvery triangle is circumscribed by some circle of diameter D, say, and circumscribes another circle of smaller diameter d. For a right triangle, d + D equals the sum of two side lengths of the triangle. Why?\u201d<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/12\/More-Right-Triangle-Magic-220619.pdf\">More Right Triangle Magic<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>James Tanton asked to prove the following surprising property of a right triangle and its circumscribed and inscribed circles. \u201cEvery triangle is circumscribed by some circle of diameter D, say, and circumscribes another circle of smaller diameter d. For a right triangle, d + D equals the sum of two side lengths of the triangle. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[43,13],"class_list":["post-3404","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-james-tanton","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3404","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=3404"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3404\/revisions"}],"predecessor-version":[{"id":3405,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3404\/revisions\/3405"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}