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2019 AMC 12B Question 6

AMC12 · 2019 AMC 12B

Question 6

In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\triangle ABC$ is $50$ units and the area of $\triangle ABC$ is $100$ square units?
  1. $0$
  2. $2$
  3. $4$
  4. $8$
  5. infinitely many