Problem 114

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Problem 114: (2019 AMC 10b, 23; 12b 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 $\omega$? $\textbf{(A) }\frac{83\pi}{8}\qquad$ $\textbf{(B) }\frac{21\pi}{2}\qquad$ $\textbf{(C) } \frac{85\pi}{8}\qquad$ $\textbf{(D) }\frac{43\pi}{4}\qquad$ $\textbf{(E) }\frac{87\pi}{8}$

Solution

Exercise 114: Solution

Points $A(4,10)$ and $B(10,2)$ 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 $\omega$?

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