IMO 1986 LL BEL5

Let ABC and DEF be acute-angled triangles. Write d = EF,

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IMO 1986 LL BEL5

Origin: BEL

Problem

Let ABC and DEF be acute-angled triangles. Write d = EF, e = FD, f = DE. Show that there exists a point P in the interior of ABC for which the value of the expression d\cdotAP +e\cdotBP +f \cdotCP attains a minimum.