tag:blogger.com,1999:blog-6933544261975483399.post1594403617163958995..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 988: Right Triangle, Cevians, Angles, 30 Degrees, Triple AngleAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-51124977605433438162022-12-05T09:25:38.571-08:002022-12-05T09:25:38.571-08:00Thank you Joaquim
Best Rgds
SumithThank you Joaquim<br /><br />Best Rgds<br /><br />SumithAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-47908691081754778412022-12-04T13:39:36.886-08:002022-12-04T13:39:36.886-08:00Sumith, congratulations for your solution. Certain...Sumith, congratulations for your solution. Certainly difficult to find. Best Regads, Joaquim Maia, BrazilAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-39282307509366772292020-02-12T22:14:20.234-08:002020-02-12T22:14:20.234-08:00A slightly modified approach
Mark X on AD extende...A slightly modified approach<br /><br />Mark X on AD extended and Y on AC such that EA = EX = EY<br />Now E is the centre of circle AXY and so < XEY = 2 X < XAY = 60<br />Hence Tr. XEY is equilateral and EA = EX = EY = XY<br /><br />Now < ADE = 3α – (60+ α) = 2α – 60 and so < XED = (2α – 60) – (α – 30) = α – 30 = < EAX<br />Therefore XE^2 = XD.XA = XY^2 and so < XYD = < XAY = 30<br /><br />But < YCD = 90-α = < YXD hence CDXY is concyclic and so < DCX = 30 and hence XY = XC<br /><br />It follows that Y is the centre of Tr. CEY and so x = < EXY = 60/2 = 30<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-63711015840385233842016-02-13T07:46:27.598-08:002016-02-13T07:46:27.598-08:00http://users.sch.gr/mnannos/wp-content/uploads/201...http://users.sch.gr/mnannos/wp-content/uploads/2015/09/988.jpgΜιχάλης Νάννοςhttps://www.blogger.com/profile/02379101429577964881noreply@blogger.com