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April 20th, 2019, 05:51 AM   #1
Joined: Apr 2019
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Red face 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.
nikolvdimitrova is offline  
April 24th, 2019, 10:39 AM   #2
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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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