My Math Forum Show that a triangle is right angled

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 April 20th, 2019, 05:51 AM #1 Newbie   Joined: Apr 2019 From: Bulgaria Posts: 5 Thanks: 0 Show that a triangle is right angled In △ABC (not isosceles) CH, CL and CM are respectively height, bisector and median. Show that ∠ACB=90 degrees if and only if ∠HCL=∠MCL. I think that I have to show that △MCB (or △ACM) is isosceles, but I can't figure it out. I will be very grateful if you help me.
 April 24th, 2019, 10:39 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,034 Thanks: 2269 If angle ACB = 90°, MA, MB and MC are equal radii of the circumcircle of triangle ABC, so triangles MCA and MCB are isosceles.

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