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triangle inside another, bisectors

Source: VTRMC 2006 P6

June 5, 2021
geometryTriangles

Problem Statement

In the diagram below, BPBP bisects ∠ABC\angle ABC, CPCP bisects ∠BCA\angle BCA, and PQPQ is perpendicular to BCBC. If BQ⋅QC=2PQ2BQ\cdot QC=2PQ^2, prove that AB+AC=3BCAB+AC=3BC. https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOC8zL2IwZjNjMDAxNWEwMTc1ZGNjMTkwZmZlZmJlMGRlOGRhYjk4NzczLnBuZw==&rn=VlRSTUMgMjAwNi5wbmc=
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