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Geo probability...with trapezoids? That's new. (BMT 2019 Geo #7)

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May 12, 2019
geometrytrapezoidprobability

Problem Statement

Points A,B,C,D A, B, C, D are vertices of an isosceles trapezoid, with AB‾ \overline{AB} parallel to CD‾ \overline{CD} , AB=1 AB = 1 , CD=2 CD = 2 , and BC=1 BC = 1 . Point E E is chosen uniformly and at random on CD‾ \overline{CD} , and let point F F be the point on CD‾ \overline{CD} such that EC=FD EC = FD . Let G G denote the intersection of AE‾ \overline{AE} and BF‾ \overline{BF} , not necessarily in the trapezoid. What is the probability that ∠AGB>30∘ \angle AGB > 30^\circ ?
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