Question 7
(IND 4) Circles $G,G_1,G_2$ are three circles related to each other as follows: Circles $G_1$ and $G_2$ are externally tangent to one another at a point $W$ and both these circles are internally tangent to the circle $G$. Points $A,B,C$ are located on the circle $G$ as follows: Line $BC$ is a direct common tangent to the pair of circles $G_1$ and $G_2$, and line $WA$ is the transverse common tangent at $W$ to $G_1$ and $G_2$, with $W$ and $A$ lying on the same side of the line $BC$. Prove that $W$ is the incenter of the triangle $ABC$.