Prove that for any interior point of a triangle the sum of squares of distances from it to the sides of a triangle is not less than $\frac{4S^2}{9R^2}$.
HIDE: about S,R they are not defined, but I suppose they mean it's area and circumradii respectivelyProblem
Source: 2011 XIV All-Ukrainian Tournament of Young Mathematiciansm Qualifying p9
Tags: geometry, geometric inequality, Ukrainian TYM