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There exist P such that X attains a minimum-IMO Long List P5

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August 28, 2010
functiongeometry proposedgeometry

Problem Statement

Let ABCABC and DEFDEF be acute-angled triangles. Write d=EF,e=FD,f=DE.d = EF, e = FD, f = DE. Show that there exists a point PP in the interior of ABCABC for which the value of the expression X=d⋅AP+e⋅BP+f⋅CPX=d \cdot AP +e \cdot BP +f \cdot CP attains a minimum.
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