Problem

Christmas Contest - Team Round - Problem 30

Let $\ell_1$ and $\ell_2$ be perpendicular lines intersecting at $O$ . Let $A$ , $B$ , $C$ be different points on $\ell_2$ , appearing in that order and all on the same side of $O$ . Let $OA=10$ , $OB=26$ , and $OC=35$ .

Let $\omega_1$ be the circle passing through $A$ and $B$ tangent to $\ell_1$ . Let $\omega_2$ be the circle, whose center is on the opposite side than that of $\omega_1$ from $\ell_2$ , that passes through $A$ and $C$ and tangent to $\ell_1$ .

Find the length of the common chord of the two circles, the answer is an integer.

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Category: Christmas Contest Team Round
Points: 7
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