tag:blogger.com,1999:blog-6933544261975483399.post1016652375832309818..comments2024-03-19T00:02:30.728-07:00Comments on Go Geometry (Problem Solutions): Problem 420. Triangle, Angles, Altitude, Sides, MeasurementAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-80273575699378510332023-12-10T00:22:22.251-08:002023-12-10T00:22:22.251-08:00[For easy typing, I use a instead of alpha]
cosa=B...[For easy typing, I use a instead of alpha]<br />cosa=BD/c<br />cos3a=BD/3c<br />cos3a/cosa=1/3<br />4(cosa)^2-3=1/3<br />(cosa)^2=5/6<br />(sina)^2=1/6<br />(1/c)^2=1/6<br />c=sqrt6<br /><br />In triangle BDC<br />sin3a=x/3c<br />3sina-4(sina)^3=x/3c<br />3/c-4(1/c)^3=x/3c<br />3c^2-4=(x*c^2)/3<br />18-4=2x<br />x=7Marconoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-51369471828405332782016-06-18T00:28:23.843-07:002016-06-18T00:28:23.843-07:00Problem 420
Suppose that the point E is symmetric...Problem 420<br />Suppose that the point E is symmetric of A with respect to the D. Then BE is the bisector of the angle ABC.Is c/3c=2/(x-1) or x=7.<br />APOSTOLIS MANOLOUDIShttps://www.blogger.com/profile/15561495997090211148noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-58102951717970982972015-09-08T03:13:41.681-07:002015-09-08T03:13:41.681-07:00Let AD = AE, E being on DC.
BE bisects < ABC,...Let AD = AE, E being on DC. <br /><br />BE bisects < ABC, hence c/3c = 2/(x-1) from which we have x = 7<br /><br />Sumith Peiris<br />Moratuwa<br />Sri Lanka Sumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-78531631103921461212010-01-19T18:22:46.919-08:002010-01-19T18:22:46.919-08:00Another way would be to extend AB to E such that B...Another way would be to extend AB to E such that BE=3c. Now it's easy to see that Tr. EAC is isosceles with BD // to altitude from E to AC which gives us: c/4c= 1/((x+1)/2) or x=7<br />AjitAjithttps://www.blogger.com/profile/00611759721780927573noreply@blogger.com