MathDB

Parallel lines in two-circle configuration

Source: Francophone 2024, Senior P3

April 4, 2024

geometrygeometry proposedcircumcircle

Problem Statement

Let

ABC

be an acute triangle,

\omega

its circumcircle and

O

its circumcenter. The altitude from

A

intersects

\omega

in a point

D \ne A

and the segment

AC

intersects the circumcircle of

OCD

in a point

E \ne C

. Finally, let

M

be the midpoint of

BE

. Show that

DE

is parallel to

OM

.

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