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AIME 2005a Problem 7

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In quadrilateral ABCD, BC=8, CD=12, AD=10,ABCD,\ BC=8,\ CD=12,\ AD=10, and m∠A=m∠B=60∘.m\angle A= m\angle B = 60^\circ. Given that AB=p+q,AB = p + \sqrt{q}, where pp and qq are positive integers, find p+q.p+q.

Dataset text AIME 1983 to 2026. Quoted with source.

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