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1969 AMC 12 Question 28

AMC12 · 1969 AMC 12

Question 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 the squares of the distances from $P$ to the endpoints of a given diameter is $3.$ Then $n$ is:
  1. $0$
  2. $1$
  3. $2$
  4. $4$
  5. infinite