2005 AMC 12B 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 \qquad \mathrm{(B)}\ 39 \qquad \mathrm{(C)}\ 51 \qquad \mathrm{(D)}\ 60 \qquad \mathrm{(E)}\ 80 \qquad

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