IMO Shortlist 2005 problem G7


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2. travnja 2012.
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In an acute triangle ABC, let D, E, F be the feet of the perpendiculars from the points A, B, C to the lines BC, CA, AB, respectively, and let P, Q, R be the feet of the perpendiculars from the points A, B, C to the lines EF, FD, DE, respectively.

Prove that p\left(ABC\right)p\left(PQR\right) \ge \left(p\left(DEF\right)\right)^{2}, where p\left(T\right) denotes the perimeter of triangle T .
Izvor: Međunarodna matematička olimpijada, shortlist 2005