KöMaL 2015 B4746

The inscribed circle of triangle $ABC$ touches sides $BC$ , $AC$ and $AB$ at points $A_1$, $B_1$ and $C_1$, respectively. The other intersection of line segment $AA_1$ with the inscribed circle is $Q$ . The line through point $A$ parallel to $BC$ intersects the lines $A_1 C_1$ and $A_1 B_1$ at points $P$ and $R$ . Prove that $PQR\sphericalangle =B_1 QC_1\sphericalangle$.