AHSME 1969 Problem 28

Let $n$ be the number of points $P$ interior to the region bounded by a circle with radius $1$, such that the sum of squares of the distances from $P$ to the endpoints of a given diameter is $3$. Then $n$ is: $\text{(A) } 0 \text{(B) } 1 \text{(C) } 2 \text{(D) } 4 \text{(E) } \infty$