AMC 12B 2019 Problem 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 A B C is 50 units and the area of \triangle A B C is 100 square units?

Answer Choices
A. 0
B. 2
C. 4
D. 8
E. infinitely many