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computational with midpoints and areas (Greece Junior 1996 p2)

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March 16, 2020
geometryareasmidpoints

Problem Statement

In a triangle ABCABC let D,E,Z,H,GD,E,Z,H,G be the midpoints of BC,AD,BD,ED,EZBC,AD,BD,ED,EZ respectively. Let II be the intersection of BE,ACBE,AC and let KK be the intersection of HG,ACHG,AC. Prove that: a) AK=3CKAK=3CK b) HK=3HGHK=3HG c) BE=3EIBE=3EI d) (EGH)=132(ABC)(EGH)=\frac{1}{32}(ABC)
Notation (...)(...) stands for area of ........
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