My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 20th, 2019, 05:51 AM   #1
Newbie
 
Joined: Apr 2019
From: Bulgaria

Posts: 5
Thanks: 0

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
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.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
angled, show, triangle



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Right angled triangles and area of a triangle novelaholic Geometry 4 October 4th, 2014 11:21 AM
ABC Isosceles triangle and right-angled mared Algebra 14 January 9th, 2014 03:01 PM
Right angled triangle tva_vlad Algebra 4 October 21st, 2013 07:24 PM
Right angled triangle rakmo Algebra 3 March 29th, 2013 12:36 PM
An acute-angled triangle gabor7896 Algebra 1 October 28th, 2009 04:56 PM





Copyright © 2019 My Math Forum. All rights reserved.