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Part of 2014 Tuymaada Olympiad

Problems(1)

Midpoint of altitude, of a segment and the circumc. are coll

Source: Tuymaada 2014, Day 1, Problem 3 Juniors, Problem 2 Seniors

7/12/2014
The points KK and LL on the side BCBC of a triangle △ABC\triangle{ABC} are such that BAK^=CAL^=90∘\widehat{BAK}=\widehat{CAL}=90^\circ. Prove that the midpoint of the altitude drawn from AA, the midpoint of KLKL and the circumcentre of △ABC\triangle{ABC} are collinear.
(A. Akopyan, S. Boev, P. Kozhevnikov)
geometrygeometric transformationhomothetyreflectiongeometry unsolvedTuymaada