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prove two lines are perpendiculars

Source: Mathematics Regional Olympiad of Mexico Southeast 2015 P2

October 26, 2021
geometryaltitudes

Problem Statement

In a acutangle triangle ABC,∠B>∠CABC, \angle B>\angle C. Let DD the foot of the altitude from AA to BCBC and EE the foot of the perpendicular from DD to ACAC. Let FF a point in DEDE. Prove that AFAF and BFBF are perpendiculars if and only if EF⋅DC=BD⋅DEEF\cdot DC=BD\cdot DE.
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