Steiner-LehumsTheorem revisited
by luimichael, Mar 15, 2017, 9:43 AM
In 
, if the angle bisectors of 
and 
are the same, then 
=
.
This is the famous Steiner_Lehmus Theorem. Recently when I calculated the length of angle bisector of a triangle I found a direct proof of the theorem.
, if the angle bisectors of 
and 
are the same, then 
=
.This is the famous Steiner_Lehmus Theorem. Recently when I calculated the length of angle bisector of a triangle I found a direct proof of the theorem.
.
.
and 
.
.
and 
and 
.
![$(a+b+c)(b-c)[a^2+a^2(b+c)+3abc+bc(b+c)]=0$](http://latex.artofproblemsolving.com/9/9/c/99c01e655da40a40438da1364f7e66d4bc203918.png)
because the other two factors are positive.
.
September 2020
January 2020