Problem #PRU-65321

Problems Algebra Mean values Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Algebraic inequalities and systems of inequalities Quadratic inequalites (several variables) Probability and statistics Statistics

14–16 4.0

Problem

The point $O$ , lying inside the triangle $A B C$ , is connected by segments with the vertices of the triangle. Prove that the variance of the set of angles $A O B$ , $A O C$ and $B O C$ is less than a) $10 π^{2} / 27$ ; b) $2 π^{2} / 9$ .

To see the solution register and get verified.