Let ABC be a triangle with AB=CB. Let C′ be a point on the ray [AB such that AC′=CB. Let A′ be a point on the ray [CB such that CA′=AB. Let the circumcircles of triangles ABA′ and CBC′ intersect at a point Q (apart from B). Prove that the line BQ bisects the segment CA.
Darij geometrycircumcirclepower of a pointradical axisgeometry proposed