MathDB

2

Part of 2020 Czech and Slovak Olympiad III A

Problems(1)

[BZX] + [CZY]> 2 [XY Z], area nequality

Source: 2020 Czech and Slovak Olympiad III A p2

11/24/2020
The triangle ABCABC is given. Inside its sides ABAB and ACAC, the points XX and YY are respectively selected Let ZZ be the intersection of the lines BYBY and CXCX. Prove the inequality [BZX]+[CZY]>2[XYZ][BZX] + [CZY]> 2 [XY Z], where [DEF][DEF] denotes the content of the triangle DEFDEF.
(David Hruska, Josef Tkadlec)
geometrygeometric inequalityarea of a triangle