Orthogonal Circles

两个圆 $O$and $Q$are orthogonal: their radii are perpendicular at their intersection point $P,$as shown above. Then the line $AD$is drawn such that it passes through both centers and intersects the arcs at points $B$and $C.$

If $AB = 10$and $CD = 24$, what is the length of the red segment $BC?$