tag:blogger.com,1999:blog-6933544261975483399.post5512124808437205484..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1522: Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. Difficulty Level: High School.Antonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6933544261975483399.post-32444568307050246982023-05-20T02:27:49.159-07:002023-05-20T02:27:49.159-07:00BD/BC = AD/AC = 1/2 implies BA is the (external) a...BD/BC = AD/AC = 1/2 implies BA is the (external) angle bisector of DBC.<br />2a+2a+a=180, a=36, ABC = 3a = 108.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-75237428898420853022023-03-08T09:08:17.818-08:002023-03-08T09:08:17.818-08:00< ABC = 3@ = 108< ABC = 3@ = 108Sumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-57527868325197472352023-03-08T01:56:12.063-08:002023-03-08T01:56:12.063-08:00Let E be the mid point of BC. Let <DBC = @ so t...Let E be the mid point of BC. Let <DBC = @ so that < ABD = 2@<br /><br />Now BE = EC = BD<br />So Triangle BDE is isosceles and <BED = <BDE = 90 - @/2<br /><br />From the midpoint theorem for Triangle ABC, <br />DE//AB so < ABD = 2@ = < BDE = 90 - @/2<br />Hence 5@/2 = 90 and so @ = 36<br /><br />Therefore < ABD = 2@ = 72<br /><br />Sumith Peiris<br />Moratuwa<br />Sri Lanka Sumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.com