2019 AMC 12B Problem 20

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?

\textbf{(A) }\frac{83\pi}{8}\qquad\textbf{(B) }\frac{21\pi}{2}\qquad\textbf{(C) } \frac{85\pi}{8}\qquad\textbf{(D) }\frac{43\pi}{4}\qquad\textbf{(E) }\frac{87\pi}{8}

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