{"id":1716,"date":"2020-08-08T08:57:26","date_gmt":"2020-08-08T12:57:26","guid":{"rendered":"http:\/\/josmfs.net\/?p=1716"},"modified":"2021-01-05T18:56:52","modified_gmt":"2021-01-05T23:56:52","slug":"circle-projection-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/08\/08\/circle-projection-problem\/","title":{"rendered":"Circle Projection Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1714\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/08\/Circle-Projection-Fig.jpg\" alt=\"\" width=\"200\" height=\"215\" \/>This is a nice Brainteaser from the <em>Quantum<\/em> math magazine.<\/p>\n<p>\u201cLine segment MN is the projection of a circle inscribed in a right triangle ABC onto its hypotenuse AB. Prove that angle MCN is 45\u00b0.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/08\/Circle-Projection-Problem-200802.pdf\">Circle Projection Problem<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a nice Brainteaser from the Quantum math magazine. \u201cLine segment MN is the projection of a circle inscribed in a right triangle ABC onto its hypotenuse AB. Prove that angle MCN is 45\u00b0.\u201d See the Circle Projection Problem.<\/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":[13,194],"class_list":["post-1716","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-quantum-magazine"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1716","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=1716"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1716\/revisions"}],"predecessor-version":[{"id":1947,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1716\/revisions\/1947"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}