MathDB

Just geometry

Source: Romanian District Olympiad 2024 9.4

March 10, 2024

geometryvector

Problem Statement

Let

H{}

be the orthocenter of the triangle

ABC{}

and

X{}

be the midpoint of the side

BC.

The perpendicular at

H{}

to

HX{}

intersects the sides

(AB)

and

(AC)

at

Y{}

and

Z{}

respectively. Let

O{}

be the circumcenter of

ABC{}

and

O'

be the circumcenter of

BHC.

[*]Prove that

HY=HZ.

[*]Prove that

\overrightarrow{AY}+\overrightarrow{AZ}=2\overrightarrow{OO'}.

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