Question 185
In a triangle $\triangle ABC$ points $L$, $P$ and $Q$ lie on the segments $AB$, $AC$ and $BC$, respectively, and are such that $PCQL$ is a parallelogram. The circle with center the midpoint $M$ of the segment $AB$ and radius $CM$ and the circle of diameter $CL$ intersect for the second time at point $T$. Prove that the lines $AQ$, $BP$ and $LT$ intersect in a point.