MathDB
2021 USMCA National Championship #22

Source:

May 9, 2021

Problem Statement

Let ABCABC be a triangle with AB=20,AC=21,AB=20, AC=21, and ∠BAC=90∘.\angle BAC = 90^{\circ}. Suppose Γ1\Gamma_1 is the unique circle centered at BB and passing through A,A, and Γ2\Gamma_2 is the unique circle centered at CC and passing through A.A. Points EE and FF are selected on Γ1\Gamma_1 and Γ2,\Gamma_2, respectively, such that E,A,FE, A, F are collinear in that order. The tangent to Γ1\Gamma_1 at EE and the tangent to Γ2\Gamma_2 at FF intersect at PP. Given that PA⊥BCPA \bot BC, compute the area of PBCPBC.
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