{"id":2639,"date":"2022-04-02T08:57:28","date_gmt":"2022-04-02T12:57:28","guid":{"rendered":"https:\/\/josmfs.net\/?p=2639"},"modified":"2024-04-06T14:49:32","modified_gmt":"2024-04-06T18:49:32","slug":"an-intercept-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/04\/02\/an-intercept-problem\/","title":{"rendered":"An Intercept Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2637\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/04\/Intercept-Problem-Fig2.jpg\" alt=\"\" width=\"255\" height=\"91\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/04\/Intercept-Problem-Fig2.jpg 508w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/04\/Intercept-Problem-Fig2-300x107.jpg 300w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/>This is a straight-forward problem by Geoffrey Mott-Smith from 1954.<\/p>\n<p>\u201cThree tangent circles of equal radius <em>r<\/em> are drawn, all centers being on the line OE. From O, the outer intersection of this axis with the left-hand circle, line OD is drawn tangent to the right-hand circle. What is the length, in terms of <em>r<\/em>, of AB, the segment of this tangent which forms a chord in the middle circle?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Intercept-Problem-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/04\/Intercept-Problem-211027.pdf\">An Intercept Problem<\/a> for solutions.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a straight-forward problem by Geoffrey Mott-Smith from 1954. \u201cThree tangent circles of equal radius r are drawn, all centers being on the line OE. From O, the outer intersection of this axis with the left-hand circle, line OD is drawn tangent to the right-hand circle. What is the length, in terms of r, [&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":[40,239],"class_list":["post-2639","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-analytic-geometry","tag-mott-smith"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2639","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=2639"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2639\/revisions"}],"predecessor-version":[{"id":3630,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2639\/revisions\/3630"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}