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3 points collinear, lie on line perpendicular to Euler line

Source: 2014 Oral Moscow Geometry Olympiad grades 10-11 p4

August 9, 2019

geometryEuler LinecollinearCentroidorthocenterperpendicular

Problem Statement

The medians

AA_0, BB_0

, and

CC_0

of the acute-angled triangle

ABC

intersect at the point

M

, and heights

AA_1, BB_1

and

CC_1

at point

H

. Tangent to the circumscribed circle of triangle

A_1B_1C_1

C_1

intersects the line

A_0B_0

at the point

C'

. Points

A'

and

B'

are defined similarly. Prove that

A', B'

and

C'

lie on one line perpendicular to the line

MH