{"id":2016,"date":"2021-02-06T08:30:52","date_gmt":"2021-02-06T13:30:52","guid":{"rendered":"http:\/\/josmfs.net\/?p=2016"},"modified":"2021-02-06T08:30:52","modified_gmt":"2021-02-06T13:30:52","slug":"three-equal-circles","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/02\/06\/three-equal-circles\/","title":{"rendered":"Three Equal Circles"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2014\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Equal-Circles-Fig2.jpg\" alt=\"\" width=\"200\" height=\"208\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Equal-Circles-Fig2.jpg 401w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Equal-Circles-Fig2-288x300.jpg 288w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Here is a problem from the <em>Quantum<\/em> magazine, only this time from the \u201cChallenges\u201d section (these are expected to be a bit more difficult than the Brainteasers).<\/p>\n<p>\u201cThree circles with the same radius <em>r<\/em> all pass through a point <em>H<\/em>.\u00a0 Prove that the circle passing through the points where the pairs of circles intersect (that is, points <em>A<\/em>, <em>B<\/em>, and <em>C<\/em>) also has the same radius <em>r<\/em>.\u201d<\/p>\n<p>Indeed, I found this quite challenging.\u00a0 It took me several weeks to work out my approach and details.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/02\/Three-Equal-Circles-200525.pdf\">Three Equal Circles<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a problem from the Quantum magazine, only this time from the \u201cChallenges\u201d section (these are expected to be a bit more difficult than the Brainteasers). \u201cThree circles with the same radius r all pass through a point H.\u00a0 Prove that the circle passing through the points where the pairs of circles intersect (that [&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-2016","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\/2016","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=2016"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2016\/revisions"}],"predecessor-version":[{"id":2017,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2016\/revisions\/2017"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}