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collinear wanted, intersecting circles and tangents related

Source: 2010 Oral Moscow Geom3try Olympiad grades 8-9 p3

August 16, 2020

geometrycirclescollinear

Problem Statement

Two circles

w_1

and

w_2

intersect at points

A

and

B

. Tangents

\ell_1

and

\ell_2

respectively are drawn to them through point

A

. The perpendiculars dropped from point

B

\ell_2

and

\ell_1

intersects the circles

w_1

and

w_2

, respectively, at points

K

and

N

. Prove that points

K, A

and

N

lie on one straight line.