Question 188
Let $\Gamma_2$ be a circle contained in the interior of another circle $\Gamma_1$ on the plane. Prove that there exists a point $P$ on the plane satisfying the following conditions: if $\ell$ is a line that does not contain $P$, that intersects $\Gamma_1$ at two different points $A, B$, and that intersects $\Gamma_2$ at two different points $C, D$ (so that $A, C, D, B$ lie in order on $\ell$), then $\angle APC = \angle DPB$.