MathDB

collinear, intersecting circles related

Source: 2009 Cuba 2.6

August 27, 2024

geometrycollinear

Problem Statement

Let

\omega_1

and

\omega_2

be circles that intersect at points

A

and

B

and let

O_1

and

O_2

be their respective centers. We take

M

in

\omega_1

and

N

in

\omega_2

on the same side as

B

with respect to segment

O_1O_2

, such that

MO_1\parallel BO_2

and

BO_1 \parallel NO_2

. Draw the tangents to

\omega_1

and

\omega_2

through

M

and

N

respectively, which intersect at

K

. Show that

A

,

B

and

K

are collinear.

Back to Problems View on AoPS