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angle bisector perpendicular to the median, twice in the same figure

Source: 2013 Oral Moscow Geometry Olympiad grades 8-9 p1

August 14, 2019
geometryangle bisectorperpendicularmedian

Problem Statement

In triangle ABCABC the angle bisector AKAK is perpendicular on the median is CLCL. Prove that in the triangle BKLBKL also one of angle bisectors are perpendicular to one of the medians.