{"id":2494,"date":"2021-12-11T07:56:56","date_gmt":"2021-12-11T12:56:56","guid":{"rendered":"https:\/\/josmfs.net\/?p=2494"},"modified":"2021-12-11T07:56:56","modified_gmt":"2021-12-11T12:56:56","slug":"ubiquitous-radius-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/12\/11\/ubiquitous-radius-problem\/","title":{"rendered":"Ubiquitous Radius Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2492\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/12\/Ubiquitous-Radius-Fig2.jpg\" alt=\"\" width=\"202\" height=\"129\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/12\/Ubiquitous-Radius-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/12\/Ubiquitous-Radius-Fig2-300x191.jpg 300w\" sizes=\"auto, (max-width: 202px) 100vw, 202px\" \/>This is an interesting problem from Posamentier and Lehmann\u2019s <em>Mathematical Curiosities<\/em>.<\/p>\n<p>\u201cIn the figure we have a semicircle with the point <em>P <\/em>randomly placed on the diameter. Points <em>A <\/em>and <em>B <\/em>are situated on the circle such that they form angles of 60\u00b0 with the diameter as shown in the figure. This problem asks us to show that the length of <em>AB <\/em>is equal to the radius of the semicircle.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/12\/Ubiquitous-Radius-Problem-211028.pdf\">Ubiquitous Radius Problem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is an interesting problem from Posamentier and Lehmann\u2019s Mathematical Curiosities. \u201cIn the figure we have a semicircle with the point P randomly placed on the diameter. Points A and B are situated on the circle such that they form angles of 60\u00b0 with the diameter as shown in the figure. This problem asks us [&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":[132,13],"class_list":["post-2494","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-alfred-posamentier","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2494","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=2494"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2494\/revisions"}],"predecessor-version":[{"id":2495,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2494\/revisions\/2495"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}