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The segments divide the parallelogram into four triangles

Source: Austrian Mathematical Olympiad 2003, Part 1, P4

June 18, 2011

geometryparallelogramratiogeometry proposed

Problem Statement

In a parallelogram

ABCD

, points

E

and

F

are the midpoints of

AB

and

BC

, respectively, and

P

is the intersection of

EC

and

FD

. Prove that the segments

AP,BP,CP

and

DP

divide the parallelogram into four triangles whose areas are in the ratio

1 : 2 : 3 : 4