MathDB

21

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

(cevian) triangle area inequality with products, = iff AA',BB'CC' concurrent

Source: Sharygin 2006 X-XI CR 21

8/26/2019
On the sides AB,BC,CAAB, BC, CA of triangle ABCABC, points C′,A′,B′C', A', B' are taken. Prove that for the areas of the corresponding triangles, the inequality holds: SABCSA′B′C′2≥4SAB′C′SBC′A′SCA′B′S_{ABC}S^2_{A'B'C'}\ge 4S_{AB'C'}S_{BC'A'}S_{CA'B'} and equality is achieved if and only if the lines AA′,BB′,CC′AA', BB', CC' intersect at one point.
concurrencyconcurrentCevianareasarea of a trianglegeometric inequalitygeometry