MathDB

3

Part of 1999 Mexico National Olympiad

Problems(1)

hexagon area = 1/3 triangle area, plus concurrency question

Source: Mexican Mathematical Olympiad 1999 OMM P3

7/28/2018
A point PP is given inside a triangle ABCABC. Let D,E,FD,E,F be the midpoints of AP,BP,CPAP,BP,CP, and let L,M,NL,M,N be the intersection points of BF BF and CE,AFCE, AF and CD,AECD, AE and BDBD, respectively. (a) Prove that the area of hexagon DNELFMDNELFM is equal to one third of the area of triangle ABCABC. (b) Prove that DL,EMDL,EM, and FNFN are concurrent.
geometryareasconcurrency