KZ-MO 2019 Problem 6

The tangent line $l$ to the circumcircle of an acute triangle $ABC$ intersects the lines $AB, BC$ , and $CA$ at points $C', A'$ and $B'$ , respectively. Let $H$ be the orthocenter of a triangle $ABC$ . On the straight lines A'H, B′H and C'H, respectively, points $A_1, B_1$ and $C_1$ (other than $H$ ) are marked such that $AH = AA_1, BH = BB_1$ and $CH = CC_1$ . Prove that the circumcircles of triangles $ABC$ and $A_1B_1C_1$ are tangent.