Question

If triangle ABC is isosceles with AB=AC and C(O,r) is the incircle of the triangle ABC touching BC at L ,prove that L bisects BC
Complete explanation with the figure is required.

Answer 1

Since tangents from the same external points are equal,

PB=BLand

QC=LC

But, AB=AC. (given)

AP+PB=AQ+QC

AP+BL=AQ+CL

So,BL=CL

Therefore,L bisects BC