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altitudes of ABC if angle bisectors of DEF, converse of incenter property

Source: Indonesia INAMO Shortlist 2010 G8

August 27, 2021
geometryangle bisectoralttiudesincenter

Problem Statement

Given an acute triangle ABCABC and points DD, EE, FF on sides BCBC, CACA and ABAB, respectively. If the lines DADA, EBEB and FCFC are the angle bisectors of triangle DEFDEF, prove that the three lines are the altitudes of triangle ABCABC.
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