MathDB
Orz Orz Orz Orz Orz geometry

Source: China MO 2023 P2

December 29, 2022
geometry

Problem Statement

Let △ABC\triangle ABC be an equilateral triangle of side length 1. Let D,E,FD,E,F be points on BC,AC,ABBC,AC,AB respectively, such that DE20=EF22=FD38\frac{DE}{20} = \frac{EF}{22} = \frac{FD}{38}. Let X,Y,ZX,Y,Z be on lines BC,CA,ABBC,CA,AB respectively, such that XY⊥DE,YZ⊥EF,ZX⊥FDXY\perp DE, YZ\perp EF, ZX\perp FD. Find all possible values of 1[DEF]+1[XYZ]\frac{1}{[DEF]} + \frac{1}{[XYZ]}.
Back to ProblemsView on AoPS