1992 AHSME Problem 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 of the circle. If \angle{APD}=60^\circ and BP=8, then r^2=

\text{(A) } 70\quad \text{(B) } 71\quad \text{(C) } 72\quad \text{(D) } 73\quad \text{(E) } 74

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.