Problem

Source: Iran MO Third Round 2022 Mid-Terms P2

Tags: geometry, circumcircle, Iran, Miquel point, geometry proposed



In the triangle ABC, variable points D,E,F are on the sides[lines] BC,CA,AB respectively so the triangle DFE is similar to the triangle ABC in this order. Circumcircles of BDF and CDE intersect respectively the circumcircle of ABC at P and Q for the second time. Prove that the circumcircle of DPQ passes through a fixed point.