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Find the locus of the intersection point

Source: Turkey IMO TST 1995 #3

July 8, 2011

geometrycircumcirclegeometry unsolved

Problem Statement

Let

D

be a point on the small arc

AC

of the circumcircle of an equilateral triangle

ABC

, different from

A

and

C

. Let

E

and

F

be the projections of

D

onto

BC

and

AC

respectively. Find the locus of the intersection point of

EF

and

OD

, where

O

is the center of

ABC