1957 AHSME Problem 46

Two perpendicular chords intersect in a circle. The segments of one chord are 3 and 4; the segments of the other are 6 and 2. Then the diameter of the circle is:

\textbf{(A)}\ \sqrt{89}\qquad \textbf{(B)}\ \sqrt{56}\qquad \textbf{(C)}\ \sqrt{61}\qquad \textbf{(D)}\ \sqrt{75}\qquad \textbf{(E)}\ \sqrt{65}

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