KURSCHAK 1971 Problem 1

A straight line cuts the side $AB$ of the triangle $ABC$ at $C_1$ , the side $AC$ at $B_1$ and the line $BC$ at $A_1$ . $C_2$ is the reflection of $C_1$ in the midpoint of $AB$ , and $B_2$ is the reflection of $B_1$ in the midpoint of $AC$ . The lines $B_2C_2$ and $BC$ intersect at $A_2$ . Prove that $$\frac{sen B_1A_1C}{sen C_2A_2B} = \frac{B_2C_2}{B_1C_1}$$