{"id":3373,"date":"2023-11-11T13:24:12","date_gmt":"2023-11-11T18:24:12","guid":{"rendered":"https:\/\/josmfs.net\/?p=3373"},"modified":"2023-11-11T13:24:12","modified_gmt":"2023-11-11T18:24:12","slug":"circles-in-circles","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/11\/11\/circles-in-circles\/","title":{"rendered":"Circles in Circles"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3371\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Circles-in-Circles-Fig2.jpg\" alt=\"\" width=\"200\" height=\"199\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Circles-in-Circles-Fig2.jpg 401w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Circles-in-Circles-Fig2-300x300.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Circles-in-Circles-Fig2-150x150.jpg 150w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Here is another problem from the \u201cChallenges\u201d section of the <em>Quantum<\/em> magazine.<\/p>\n<p>\u201cInside a circle there are two intersecting circles. One of them touches the big circle in point A, the other in point B. Prove that if segment AB meets the smaller circles at one of their common points, then the sum of their radii equals the radius of the big circle. Is the converse true?\u00a0 (A. Vesyolov)\u201d<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Circles-in-Circles-200409.pdf\">Circles in Circles<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another problem from the \u201cChallenges\u201d section of the Quantum magazine. \u201cInside a circle there are two intersecting circles. One of them touches the big circle in point A, the other in point B. Prove that if segment AB meets the smaller circles at one of their common points, then the sum of their [&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":[13,194],"class_list":["post-3373","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\/3373","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=3373"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3373\/revisions"}],"predecessor-version":[{"id":3374,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3373\/revisions\/3374"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}