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

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

July 12, 2014

geometrygeometric transformationhomothetyreflectiongeometry unsolvedTuymaada

Problem Statement

The points

K

and

L

on the side

BC

of a triangle

\triangle{ABC}

are such that

\widehat{BAK}=\widehat{CAL}=90^\circ

. Prove that the midpoint of the altitude drawn from

A

, the midpoint of

KL

and the circumcentre of

\triangle{ABC}

are collinear.
(A. Akopyan, S. Boev, P. Kozhevnikov)