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concyclic , touchpoints of incircle related

Source: All-Russian MO 1994 Regional (R4) 11.3

August 26, 2024

geometryConcyclicincircle

Problem Statement

A circle with center

O

is tangent to the sides

AB

,

EF

,

N

of a triangle

ABC

at points

E,F,D

respectively. The lines

AO

and

CO

meet

EF

at points

N

and

M

. Prove that the circumcircle of triangle

OMN

and points

O

and

D

lie on a line.

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