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Source: 2023 Thailand Online MO P4

February 12, 2023
geometry

Problem Statement

Let ABCABC be a triangle, and let DD and D1D_1 be points on segment BCBC such that BD=CD1BD = CD_1. Construct point EE such that EC⊥BCEC\perp BC and ED⊥ACED\perp AC. Similarly, construct point FF such that FB⊥BCFB\perp BC and FD⊥ABFD\perp AB. Prove that EF⊥AD1EF\perp AD_1.
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