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Intersection of bisector and altitude

Source: Kyiv City MO 2024 Round 1, Problem 9.2/10.2

January 28, 2024
geometryangle bisector

Problem Statement

Let BL,ADBL, AD be the bisector and the altitude correspondingly of an acute triangle ABC. They intersect at point TT. It turned out that the altitude LKLK of △ALB\triangle ALB is divided in half by the line ADAD. Prove that KT⊥BLKT \perp BL.
Proposed by Mariia Rozhkova
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