Question 129
Given $ABCD$ be a quadrilateral inscribed in a circle with center $O$, and let $P = AC \cap BD$, $BC \parallel AD$. Rays $AB$ and $DC$ intersect at the point $E$. A circle with the center $I$ is inscribed in the triangle $EBC$ and is tangent to the line $BC$ at point $T_1$. The excircle of the triangle $EAD$ with center $J$ is tangent to the side $AD$ at point $T_2$. The lines $IT_1$ and $JT_2$ intersect at the point $Q$. Prove that points $O$, $P$ and $Q$ are collinear.