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Orthocenter of BCI lies on DE

Source: Nordic Mathematical Contest 2018 Problem 3

April 10, 2018

geometry

Problem Statement

Let

ABC

be a triangle with

AB < AC

. Let

D

and

E

be on the lines

CA

and

E

, respectively, such that

CD = AB

,

BE = AC

, and

A

,

D

and

E

lie on the same side of

BC

. Let

I

be the incenter of triangle

ABC

, and let

H

be the orthocenter of triangle

BCI

. Show that

D

,

E

, and

H

are collinear.

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