Question 131
In the right trapezoid $ABCD$ the side $CD$ is perpendicular to the bases. The circle with diameter $AB$ intersects $AD$ at $A$ and $P$, and the tangent to this circle at the point $P$ intersects line $CD$ at $M$. From the point $M$ the second tangent line $l$ to our circle is drawn, touching it at the point $Q$. Prove that the line $BQ$ halves the segment $CD$.