Orthogonal Circles

Geometry Level 3

Two circles OO and QQ are orthogonal: their radii are perpendicular at their intersection point P,P, as shown above. Then the line ADAD is drawn such that it passes through both centers and intersects the arcs at points BB and C.C.

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

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