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Easy Geo involving Concyclicity

Source: German TSTST 2016 - #1

July 9, 2016

Concyclicgeometry unsolvedgeometrycirclecircles

Problem Statement

The two circles

\Gamma_1

and

\Gamma_2

with the midpoints

O_1

resp.

O_2

intersect in the two distinct points

A

and

B

. A line through

A

meets

\Gamma_1

in

C \neq A

and

\Gamma_2

in

D \neq A

. The lines

CO_1

and

DO_2

intersect in

X

. Prove that the four points

O_1,O_2,B

and

X

are concyclic.

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