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Indonesian Geometry Olympiad

Source: Indonesian National Mathematical Olympiad 2024, Problem 3

August 28, 2024

geometrycircumcircleIndonesiaorthocenterIndonesia MOInamo

Problem Statement

The triangle

ABC

has

O

as its circumcenter, and

H

as its orthocenter. The line

AH

and

BH

intersect the circumcircle of

BHD

for the second time at points

A', B', O, H

and

E

, respectively. Let

A'

and

B'

be the circumcenters of triangle

AHE

and

BHD

respectively. If

A', B', O, H

are not collinear, prove that

OH

intersects the midpoint of segment

A'B'

.

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