AHSME 1950 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: $\textbf{(A)}\ \text{A straight line }AB,1\dfrac{1}{2}\text{ inches from }A \\ \textbf{(B)}\ \text{A circle with }A\text{ as center and radius }2\text{ inches} \\ \textbf{(C)}\ \text{A circle with }A\text{ as center and radius }3\text{ inches} \\ \textbf{(D)}\ \text{A circle with radius }3\text{ inches and center }4\text{ inches from }B\text{ along } BA \\ \textbf{(E)}\ \text{An ellipse with }A\text{ as focus}$