Question 27
A circle of radius $r$ has chords $\overline{AB}$ of length $10$ and $\overline{CD}$ of length $7.$ When $\overline{AB}$ and $\overline{CD}$ are extended through $B$ and $C,$ respectively, they intersect at $P,$ which is outside the circle. If $\angle APD=60^\circ$ and $BP=8,$ then $r^2=$