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equal segments wanted, starting with intersecting circles and a parallel

Source: Czech-Polish-Slovak Junior Match 2014, Individual p1 CPSJ

March 13, 2020

equal segmentsgeometrycirclesparallelogram

Problem Statement

On the plane circles

k

and

\ell

are intersected at points

C

and

D

, where circle

k

passes through the center

L

of circle

\ell

. The straight line passing through point

D

intersects circles

k

and

\ell

for the second time at points

A

and

B

respectively in such a way that

D

is the interior point of segment

AB

. Show that

AB = AC