1991 AHSME Problem 10

Point P is 9 units from the center of a circle of radius 15. How many different chords of the circle contain P and have integer lengths?

\textbf{(A) } 11\qquad \textbf{(B) } 12\qquad \textbf{(C) } 13\qquad \textbf{(D) } 14\qquad \textbf{(E) } 29

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