KURSCHAK 2019 Problem 1

In an acute triangle $\bigtriangleup ABC$ , $AB<AC<BC$ , and $A_1,B_1,C_1$ are the projections of $A,B,C$ to the corresponding sides. Let the reflection of $B_1$ wrt $CC_1$ be $Q$ , and the reflection of $C_1$ wrt $BB_1$ be $P$ . Prove that the circumcirle of $A_1PQ$ passes through the midpoint of $BC$ .