AMC 12 2005b Problem 18

Let $A(2,2)$ and $B(7,7)$ be points in the plane. Define $R$ as the region in the first quadrant consisting of those points $C$ such that $\triangle ABC$ is an acute triangle. What is the closest integer to the area of the region $R$?

$\mathrm{(A)}\ 25 \mathrm{(B)}\ 39 \mathrm{(C)}\ 51 \mathrm{(D)}\ 60 \mathrm{(E)}\ 80$