Problem

Source: China Western Mathematical Olympiad 2008

Tags: analytic geometry, function, vector, trigonometry, calculus, derivative, geometry



Let P be an interior point of a regular n-gon $ A_1 A_2 ...A_n$, the lines $ A_i P$ meet the regular n-gon at another point $ B_i$, where $ i=1,2,...,n$. Prove that sums of all $ PA_i\geq$ sum of all $ PB_i$.