1950 AHSME Problem 49

A triangle has a fixed base AB that is 2 inches long. The median from A to side BC is 1 \frac{1}{2} inches long and can have any position emanating from A. The locus of the vertex C of the triangle is:

\begin{array}{l} \textbf{(A)}\ \text{A straight line }AB,1\frac{1}{2}\text{ inches from }A\qquad\\ \textbf{(B)}\ \text{A circle with }A\text{ as center and radius }2\text{ inches}\qquad\\ \textbf{(C)}\ \text{A circle with }A\text{ as center and radius }3\text{ inches}\qquad\\ \textbf{(D)}\ \text{A circle with radius }3\text{ inches and center }4\text{ inches from }B\text{ along }BA\qquad\\ \textbf{(E)}\ \text{An ellipse with }A\text{ as focus} \end{array}

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