Question 116
Two triangles $ABC$ and $A_1B_1C_1$ are symmetric about the center of their common incircle of radius $r$. Prove that the product of the areas of the triangles $ABC$, $A_1B_1C_1$ and the six other triangles formed by the intersecting sides of the triangles $ABC$ and $A_1B_1C_1$ is equal to $r^{16}$.