2016 AIME I #15

June 3, 2022 mathproblemsolvingskills

Circles $\omega_1$ and $\omega_2$ intersect at points $X$ and $Y$ . Line $l$ is tangent to $\omega_1$ and $\omega_2$ at $A$ and $B$ , respectively, with line $AB$ closer to point $X$ than to $Y$ . Circle $\omega$ passes through $A$ and $B$ intersecting $\omega_1$ again at $D \neq A$ and intersecting $\omega_2$ again at $C \neq B$ . The three points $C, Y,$ and $D$ are collinear, $XC = 67, XY = 47,$ and $XD = 37$ . Find $AB^2$ .

Published by mathproblemsolvingskills

I coach students preparing for MathCounts and the AMCs, and I teach using curricula published by Art of Problem Solving. View all posts by mathproblemsolvingskills

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