Question

In ΔABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that: CB : BA = CP : PA

Answer 1

In ΔABC,

∠ABC = 2∠ACB 

Let ∠ACB = x

`=>` ∠ABC = 2∠ACB = 2x

Given BP is bisector of ∠ABC

Hence ∠ABP = ∠PBC = x

Using the angle bisector theorem,

That is the bisector of an angle divides the side opposite to it in the ratio of other two sides.

Hence, CB : BA = CP : PA.