IZhO 2024 Problem 2

Circles $\Omega$ and $\Gamma$ meet at points $A$ and $B$. The line containing their centres intersects $\Omega$ and $\Gamma$ at points $P$ and $Q$, respectively, such that these points lie on the same side of the line $AB$ and point $Q$ is closer to $AB$ than point $P$. The circle $\delta$ lies on the same side of the line $AB$ as $P$ and $Q$, touches the segment $AB$ at point $D$ and touches $\Gamma$ at point $T$. The line $PD$ meets $\delta$ and $\Omega$ again at points $K$ and $L$, respectively. Prove that $\angle QTK = \angle DTL$.