August 12th, 2018, 04:08 AM  #1 
Member Joined: Oct 2012 Posts: 65 Thanks: 0  Bisectors
ABC is a triangle B' is a point in AC such that BB' is a bisector of the angle B, similarly CC' is the bisector of the angle C. Show that m(A)= 60 degree if and only if BC=BC'+CB'.

August 13th, 2018, 05:24 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,704 Thanks: 1804 
m(A) = 60 degrees if and only if AC² + AB² = BC² + AB.AC. Use the angle bisector theorem to show that BC = BC' + CB' if and only if AC² + AB² = BC² + AB.AC. 

Tags 
bisectors 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
angle bisectors open problem?  zeta275  Geometry  1  November 10th, 2017 06:14 PM 
triangle feet of bisectors  mared  Geometry  2  April 2nd, 2014 02:16 PM 