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

\textbf{(A) }0\qquad\textbf{(B) }2\qquad\textbf{(C) }4\qquad\textbf{(D) }8\qquad\textbf{(E) }\text{infinitely many}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.