UA-UMO 2021 Problem 116

The altitudes $AA_1, BB_1$ and $CC_1$ were drawn in the triangle $ABC$ . Point $K$ is a projection of point $B$ on $A_1C_1$ . Prove that the symmmedian $\vartriangle ABC$ from the vertex $B$ divides the segment $B_1K$ in half.

(Anton Trygub)