Problem #WSP-5619

Problems Geometry

Problem

In a triangle \(ABC\) we have \(AB = AC\). A circle which is internally tangent to the circumcircle of the triangle is also tangent to the sides \(AB\) and \(AC\) at the points \(P\) and \(Q\), respectively. Prove that the midpoint of \(PQ\) is the centre of the incircle of triangle \(ABC\).