Maths Olympiad Daily Problems

9 months 🥲🥲

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Two circles ωA and ωB have centers at points A and B respectively and intersect at points P and Q in such a way that A, B, P, and Q all lie on a common circle ω. The tangent to ω at P intersects ωA and ωB again at points X and Y respectively. Suppose AB = 17 and XY = 20. The sum of the radii of ωA and ωB can be expressed in the form m √ n, where m and n are positive integers, and n is not divisible by the square of any prime. Find m + n.

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