{"id":27074,"date":"2020-12-02T12:12:29","date_gmt":"2020-12-02T17:12:29","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=27074"},"modified":"2020-12-02T12:12:41","modified_gmt":"2020-12-02T17:12:41","slug":"carlyles-trick-equation-of-a-circle-whose-diameter-is-given-by-a-segment","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=27074","title":{"rendered":"Carlyle&#8217;s trick: equation of a circle whose diameter is given by a segment"},"content":{"rendered":"\n<figure class=\"wp-block-embed-twitter wp-block-embed is-type-rich is-provider-twitter\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"twitter-tweet\" data-width=\"550\" data-dnt=\"true\"><p lang=\"en\" dir=\"ltr\">Spoiler alert!<br><br>Say the diameter is a segment from A=(a,b) to B=(c,d). A point C=(x,y) on the circle forms a *right* triangle with those two points (Thales!), so the vectors AC and BC are orthogonal, so their slopes are negative reciprocals. That is,<br><br>(y-b)\/(x-a)=-(x-c)\/(y-d).<\/p>&mdash; Alex Kontorovich (@AlexKontorovich) <a href=\"https:\/\/twitter.com\/AlexKontorovich\/status\/1330704619668983809?ref_src=twsrc%5Etfw\">November 23, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-27074","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27074","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=27074"}],"version-history":[{"count":1,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27074\/revisions"}],"predecessor-version":[{"id":27075,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27074\/revisions\/27075"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=27074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=27074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=27074"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}