MathDB
XA *XB * XC >=8 d(X, AB) * d(X, BC) * d(X, AC)

Source: Polish MO Recond Round 1977 p2

September 9, 2024
geometryinequalitiesgeometric inequality

Problem Statement

Let XX be the interior point of triangle ABCABC. prove that the product of the distances of point X X from the vertices A,B,C A, B, C is at least eight times greater than the product of the distances of this point from the lines AB,BC,CA AB, BC, CA .
Back to ProblemsView on AoPS