1978 AHSME Problem 10

If \mathit{B} is a point on circle \mathit{C} with center \mathit{P}, then the set of all points \mathit{A} in the plane of circle \mathit{C} such that the distance between \mathit{A} and \mathit{B} is less than or equal to the distance between \mathit{A} and any other point on circle \mathit{C} is

\begin{array}{l} \textbf{(A) }\text{the line segment from }P \text{ to }B\qquad\\ \textbf{(B) }\text{the ray beginning at }P \text{ and passing through }B\qquad\\ \textbf{(C) }\text{a ray beginning at }B\qquad\\ \textbf{(D) }\text{a circle whose center is }P\qquad\\ \textbf{(E) }\text{a circle whose center is }B \end{array}

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