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CD contains the circumcenter O of ABC

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October 31, 2010

geometrycircumcircleperpendicular bisectorgeometry unsolved

Problem Statement

In an acute-angled triangle

ABC

,

M

and

N

are points on the sides

AC

and

BC

respectively, and

\triangle ABC

the midpoint of

MN

. The circumcircles of triangles

ACN

and

BCM

meet again at a point

D

. Prove that the line

CD

contains the circumcenter

O

of

\triangle ABC

if and only if

K

is on the perpendicular bisector of

AB.

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