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2012 PUMaC Geometry A5

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September 24, 2019
geometry

Problem Statement

Let △ABC\vartriangle ABC be a triangle with ∠BAC=45o,∠BCA=30o\angle BAC = 45^o, \angle BCA = 30^o, and AB=1AB = 1. Point DD lies on segment ACAC such that AB=BDAB = BD. Find the square of the length of the common external tangent to the circumcircles of triangles △BDC\vartriangle BDC and △ABC\vartriangle ABC.
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