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4

Part of 2003 Federal Competition For Advanced Students, Part 1

Problems(1)

The segments divide the parallelogram into four triangles

Source: Austrian Mathematical Olympiad 2003, Part 1, P4

6/18/2011
In a parallelogram ABCDABCD, points EE and FF are the midpoints of ABAB and BCBC, respectively, and PP is the intersection of ECEC and FDFD. Prove that the segments AP,BP,CPAP,BP,CP and DPDP divide the parallelogram into four triangles whose areas are in the ratio 1:2:3:41 : 2 : 3 : 4.
geometryparallelogramratiogeometry proposed