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2011 PUMaC Geometry A5 / B7

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September 24, 2019
geometry

Problem Statement

Let ℓ1\ell_1 and ℓ2\ell_2 be two parallel lines, a distance of 15 apart. Points AA and BB lie on ℓ1\ell_1 while points CC and DD lie on ℓ2\ell_2 such that ∠BAC=30∘\angle BAC = 30^\circ and ∠ABD=60∘\angle ABD = 60^\circ. The minimum value of AD+BCAD + BC is aba\sqrt b, where aa and bb are integers and bb is squarefree. Find a+ba + b.
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