Question 20
In an acute triangle $ ABC $, let $ D $, $ E $, $ F $, $ P $, $ Q $, $ R $ be the feet of perpendiculars from $ A $, $ B $, $ C $, $ A $, $ B $, $ C $ to $ BC $, $ CA $, $ AB $, $ EF $, $ FD $, $ DE $, respectively. Prove that $ p(ABC)p(PQR) \geq p(DEF)^2 $, where $ p(T) $ denotes the perimeter of triangle $ T $.