{"id":154,"date":"2023-01-18T22:12:26","date_gmt":"2023-01-18T22:12:26","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=154"},"modified":"2023-01-18T22:12:26","modified_gmt":"2023-01-18T22:12:26","slug":"a-rhombus-with-the-least-possible-perimeter","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/18\/a-rhombus-with-the-least-possible-perimeter\/","title":{"rendered":"A Rhombus with the Least Possible Perimeter"},"content":{"rendered":"\n<p>In this geometry problem circles of radius 1 and radius 2 are tangential and fit in a rhombus such that each circle is tangential to two of its sides. The rhombus has the least possible perimeter. What is the perimeter of the rhombus and the lengths of its diagonals?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"817\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circles_radii_1_and_2_in_rhombus-1024x817.png\" alt=\"\" class=\"wp-image-155\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circles_radii_1_and_2_in_rhombus-1024x817.png 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circles_radii_1_and_2_in_rhombus-300x239.png 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circles_radii_1_and_2_in_rhombus-768x613.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circles_radii_1_and_2_in_rhombus-1536x1225.png 1536w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circles_radii_1_and_2_in_rhombus-2048x1634.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In this geometry problem circles of radius 1 and radius 2 are tangential and fit in a rhombus such that each circle is tangential to two&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,5],"tags":[13,12],"class_list":["post-154","post","type-post","status-publish","format-standard","hentry","category-geogebra","category-geometry","tag-geogebra","tag-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":1,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions"}],"predecessor-version":[{"id":156,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/154\/revisions\/156"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}