Question 170
Let $\Omega$ be the incircle of $\triangle ABC$. There are two smaller circles $\omega_1$ and $\omega_2$ inside $\triangle ABC$. The circle $\omega_1$ is tangent to $\Omega$ at $P$, tangent to $BC$ at $D$, and also tangent to $AB$. The circle $\omega_2$ is tangent to $\Omega$ at $Q$, tangent to $BC$ at $E$, and also tangent to $AC$. Prove that $D, E, Q, P$ are concyclic.