MathDB

2

Part of 1977 Poland - Second Round

Problems(1)

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

Source: Polish MO Recond Round 1977 p2

9/9/2024
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 .
geometryinequalitiesgeometric inequality