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DE = DF if <BEH = <C and <CFH =<B

Source: 2015 VMEO IV Juniors 10.2 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2463156_2015_vmeo_iv

September 15, 2021
geometryequal segmentsequal angles

Problem Statement

Given a triangle ABCABC with obtuse ∠A\angle A and attitude AHAH with H∈BCH \in BC. Let E,FE,F on CACA, ABAB satisfying ∠BEH=∠C\angle BEH = \angle C and ∠CFH=∠B\angle CFH = \angle B. Let BEBE cut CFCF at DD. Prove that DE=DFDE = DF.
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