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The line AK passes through circumcenter (6)

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October 28, 2010

geometrycircumcircleperpendicular bisectorgeometry unsolved

Problem Statement

Points

M

and

N

lie on the side

BC

of the regular triangle

ABC

(

M

is between

B

and

N

), and

\angle MAN=30^\circ.

The circumcircles of triangles

AMC

and

ANB

meet at a point

K.

Prove that the line

AK

passes through the circumcenter of triangle

AMN.