1959 AHSME Problem 32

The length l of a tangent, drawn from a point A to a circle, is \frac43 of the radius r. The (shortest) distance from A to the circle is: \textbf{(A)}\ \frac{1}{2}r \qquad\textbf{(B)}\ r\qquad\textbf{(C)}\ \frac{1}{2}l\qquad\textbf{(D)}\ \frac23l \qquad\textbf{(E)}\ \text{a value between r and l.}

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