{"id":4675,"date":"2025-11-29T10:53:30","date_gmt":"2025-11-29T15:53:30","guid":{"rendered":"https:\/\/josmfs.net\/wordpress\/?p=4675"},"modified":"2025-11-29T10:53:30","modified_gmt":"2025-11-29T15:53:30","slug":"three-circles-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2025\/11\/29\/three-circles-problem\/","title":{"rendered":"Three Circles Problem"},"content":{"rendered":"

\"\"This is a problem from the 1995 AIME problems.<\/p>\n

\u201cCircles of radius 3 and 6 are externally tangent to each other and are internally tangent to a circle of radius 9. The circle of radius 9 has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.\u201d<\/p>\n

Answer<\/a>.<\/p>\n

See the Three Circles Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"

This is a problem from the 1995 AIME problems. \u201cCircles of radius 3 and 6 are externally tangent to each other and are internally tangent to a circle of radius 9. The circle of radius 9 has a chord that is a common external tangent of the other two circles. Find the square of the […]<\/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":[238,13],"class_list":["post-4675","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-aime","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4675","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=4675"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4675\/revisions"}],"predecessor-version":[{"id":4676,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4675\/revisions\/4676"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4675"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}