MathDB
SMT 2022 Geometry #6

Source:

April 1, 2023

Problem Statement

Let the incircle of △ABC\triangle ABC be tangent to AB,BC,ACAB,BC,AC at points M,N,PM,N,P, respectively. If ∡BAC=30∘\measuredangle BAC=30^\circ, find [BPC][ABC]⋅[BMC][ABC]\tfrac{[BPC]}{[ABC]}\cdot\tfrac{[BMC]}{[ABC]}, where [ABC][ABC] denotes the area of △ABC\triangle ABC.
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