AMC10 2027 - Self-practice Set 4 Question 4

Question 4

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?

$ 0 $
$ 2 $
$ 4 $
$ 8 $
Infinitely many