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Determine the position of D from condition

Source: China mathematical olympiad 1998 problem5

August 22, 2013
inequalitiesgeometryparallelogramgeometry unsolved

Problem Statement

Let DD be a point inside acute triangle ABCABC satisfying the condition DA⋅DB⋅AB+DB⋅DC⋅BC+DC⋅DA⋅CA=AB⋅BC⋅CA.DA\cdot DB\cdot AB+DB\cdot DC\cdot BC+DC\cdot DA\cdot CA=AB\cdot BC\cdot CA. Determine (with proof) the geometric position of point DD.
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