Problem

Source: V.A. Yasinsky Geometry Olympiad 2018 X-XI advanced p3 [Ukraine]

Tags: geometry, construction, Circumcenter, circumcircle, angle bisector, isosceles



Point $O$ is the center of circumcircle $\omega$ of the isosceles triangle $ABC$ ($AB = AC$). Bisector of the angle $\angle C$ intersects $\omega$ at the point $W$. Point $Q$ is the center of the circumcircle of the triangle $OWB$. Construct the triangle $ABC$ given the points $Q,W, B$. (Andrey Mostovy)