Question

In triangle ABC; angle ABC = ${90}^0$ and P is a point on AC such that $\angle$ PBC = $\angle$ PCB. Show that : BP = CP.

Answer 1

given: ABC is a right angled triangle, right angled at B.

TPT: PA = PB

proof:

in the right angled triangle ABC,

...........(1)

and

therefore in the triangle ABP;

therefore PA = PB [since in a triangle sides opposite to equal angles are equal in length]