Question 10
Two circles $w_1, w_2$ are externally tangent at a point $Q$. A common external tangent line to these circles (that doesn't pass through $Q$) is tangent to $w_1$ at a point $B$, and $BA$ is a diameter of this circle. The point $A$ belongs to the line tangent to the circle $w_2$ at a point $C$ such that $B$ and $C$ are in the same half-plane with respect to the line $AQ$. Prove that the circle $w_1$ bisects the segment $BC$.
Fig. 6.
Fig. 6.