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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: 20,622 Thanks: 2074 
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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