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An old geometry

Source: 2001 China Second Round Olympiad P1

August 11, 2019

geometry

Problem Statement

Let

O,H

be the circumcenter and orthocenter of

E,

respectively. Line

AH

and

BC

intersect at

D,

Line

BH

and

AC

intersect at

E,

Line

CH

and

AB

intersect at

F,

Line

AB

and

ED

intersect at

M,

AC

and

FD

intersect at

N.

Prove that

(1)OB\perp DF,OC\perp DE;

(2)OH\perp MN.

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