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Equal lengths on altitude

Source: Spain MO 2023 P2

March 10, 2023

geometry

Problem Statement

Let

ABC

be an acute scalene triangle with incenter

I

and orthocenter

H

. Let

M

be the midpoint of

AB

. On the line

AH

we consider points

D

and

E

, such that the line

MD

is parallel to

CI

and

ME

is perpendicular to

CI

. Prove that

AE=DH

.

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