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CD bisects arc EF

Source: ItaMO 2005, P6

March 9, 2012

geometrycircumcircleincentergreatest common divisorangle bisectorgeometry proposed

Problem Statement

Two circles

\gamma_1, \gamma_2

in a plane, with centers

A

and

B

respectively, intersect at

F

and

EF

. Suppose that the circumcircle of

ABC

intersects

\gamma_1

in

E

and

\gamma_2

in

F

, where the arc

EF

not containing

C

lies outside

\gamma_1

and

\gamma_2

. Prove that this arc

EF

is bisected by the line

CD

.

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