AMC 10 2020b Problem 8

Points $P$ and $Q$ lie in a plane with $PQ=8$. How many locations for point $R$ in this plane are there such that the triangle with vertices $P$, $Q$, and $R$ is a right triangle with area $12$ square units? $\textbf{(A)}\ 2 \textbf{(B)}\ 4 \textbf{(C)}\ 6 \textbf{(D)}\ 8 \textbf{(E)}\ 12$