{"id":1071,"date":"2017-04-23T04:00:46","date_gmt":"2017-04-23T09:00:46","guid":{"rendered":"https:\/\/trigonography.com\/?p=1071"},"modified":"2022-06-24T23:24:06","modified_gmt":"2022-06-25T04:24:06","slug":"inradius-and-circumradius-of-a-right-triangle","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=1071","title":{"rendered":"Inradius and Circumradius of a Right Triangle"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2017\/04\/trigonograph-inradiusandcircumradiusofrighttriangle.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2017\/04\/trigonograph-inradiusandcircumradiusofrighttriangle.png\" alt=\"\" width=\"480\" height=\"450\"\/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center\" style=\"font-size:16px\">Given a right triangle with legs \\(a\\) and \\(b\\), inradius \\(r\\), and circumradius \\(R\\):<\/p>\n\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt\">$$\\large (a-r) + (b-r) = 2 R \\quad\\to\\quad a + b = 2 ( R + r )$$<\/div>\n\n\n\n<p class=\"has-text-align-center\" style=\"font-size:16px\"><em style=\"color: gray;\">Motivated by <a href=\"https:\/\/math.stackexchange.com\/q\/2247599\/409\">this question<\/a> on the Mathematics Stack Exchange.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given a right triangle with legs \\(a\\) and \\(b\\), inradius \\(r\\), and circumradius \\(R\\): $$\\large (a-r) + (b-r) = 2 R \\quad\\to\\quad a + b = 2 ( R + r )$$ Motivated by this question on the Mathematics Stack Exchange.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1071","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/1071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1071"}],"version-history":[{"count":7,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/1071\/revisions"}],"predecessor-version":[{"id":1179,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/1071\/revisions\/1179"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}