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Nordic MC 2006 Q1

Source:

March 3, 2013
geometrycircumcirclegeometric transformationperpendicular bisectorangle bisectorgeometry unsolved

Problem Statement

Points B,CB,C vary on two fixed rays emanating from point AA such that AB+ACAB+AC is constant. Show that there is a point DD, other than AA, such that the circumcircle of triangle ABCABC passes through DD for all possible choices of B,CB, C.
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