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collinear, ext. tangent circles related

Source: All-Russian MO 2009 Regional 10. 4

August 27, 2024

geometrycollinear

Problem Statement

Circles

\omega_1

and

\omega_2

touch externally at the point

O

. Points

A

and

B

on the circle

\omega_1

and points

C

and

M

on the circle

CO

are such that

AC

and

BD

are common external tangents to circles. Line

AO

intersects segment

CD

at point

M

and straight line

CO

intersexts

\omega_1

again at point

N

. Prove that the points

B

,

M

and

N

lie on the same straight line.

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