Question 92
The circles $\Gamma_1$ and $\Gamma_2$ meet at $D$ and $P$. Their common tangent closest to $D$ touches $\Gamma_1$ at $A$ and $\Gamma_2$ at $B$. The line $AD$ meets $\Gamma_2$ again at $C$. Let $M$ be the midpoint of $BC$.
Prove that $\angle DPM=\angle BDC$.
Prove that $\angle DPM=\angle BDC$.