{"id":2941,"date":"2022-11-05T07:54:26","date_gmt":"2022-11-05T11:54:26","guid":{"rendered":"https:\/\/josmfs.net\/?p=2941"},"modified":"2024-04-06T09:55:38","modified_gmt":"2024-04-06T13:55:38","slug":"triangle-projection-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/11\/05\/triangle-projection-problem\/","title":{"rendered":"Triangle Projection Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2939\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/11\/Triangle-Projection-Fig2.jpg\" alt=\"\" width=\"201\" height=\"182\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/11\/Triangle-Projection-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/11\/Triangle-Projection-Fig2-300x272.jpg 300w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/>This is a Maths Item of the Month (MIOM) <a href=\"https:\/\/mei.org.uk\/maths-item-of-the-month\/\">problem<\/a> that seems opaque at first.\u00a0 (\u201cThe Maths Item of the Month is a monthly problem aimed at teachers and students of GCSE and A level Mathematics.\u201d)<\/p>\n<p>\u201cTwo fixed circles, <em>C<\/em><sub>1<\/sub> and <em>C<\/em><sub>2<\/sub>, intersect at <em>A<\/em> and <em>B<\/em>.\u00a0 <em>P<\/em> is on <em>C<\/em><sub>1<\/sub>.\u00a0 <em>PA<\/em> and <em>PB<\/em> produced meet <em>C<\/em><sub>2<\/sub> at <em>A&#8217;<\/em> and <em>B&#8217;<\/em> respectively.\u00a0 How does the length of the chord <em>A&#8217;B&#8217;<\/em> change as <em>P<\/em> moves?\u201d<\/p>\n<p>Just start noticing relationships and the answer falls out nicely.<\/p>\n<p>(MIOM problems often appear on MathsMonday and are also produced by Mathematics Education Innovation (MEI).)<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Circle-Projection-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/11\/Triangle-Projection-Problem-220909.pdf\">Triangle Projection Problem<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a Maths Item of the Month (MIOM) problem that seems opaque at first.\u00a0 (\u201cThe Maths Item of the Month is a monthly problem aimed at teachers and students of GCSE and A level Mathematics.\u201d) \u201cTwo fixed circles, C1 and C2, intersect at A and B.\u00a0 P is on C1.\u00a0 PA and PB produced [&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":[213,13],"class_list":["post-2941","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-mathsmonday","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2941","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=2941"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2941\/revisions"}],"predecessor-version":[{"id":3587,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2941\/revisions\/3587"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}