Consider an isosceles triangle $$ABC$$ with sides $$BC=30,$$ $$CA=AB=20$$. Let $$D$$ be the foot of the perpendicular from $$A$$ to $$BC$$, and let $$M$$ be the midpoint of $$AD$$. Let $$PQ$$ be a chord of the circumcircle of triangle $$ABC$$, such that $$M$$ lies on $$PQ$$ and $$PQ$$ is parallel to $$BC$$. The length of $$PQ$$ is: