Points A(6,13) and B(12,11) lie on circle \omega in the plane. Suppose that the tangent lines to \omega at A and B intersect at a point on the x-axis. What is the area of \omega ?
Answer Choices
A. \dfrac{83 \pi}{8}
B. \dfrac{21 \pi}{2}
C. \dfrac{85 \pi}{8}
D. \dfrac{43 \pi}{4}
E. \dfrac{87 \pi}{8}