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Turkey TST 1996 Problem 4, compute the ratio S_KLMN/S_ABC

Source: Turkey TST 1996 Problem 4

September 28, 2011
ratiogeometryparallelogramgeometry proposed

Problem Statement

The diagonals ACAC and BDBD of a convex quadrilateral ABCDABCD with SABC=SADCS_{ABC} = S_{ADC} intersect at EE. The lines through EE parallel to ADAD, DCDC, CBCB, BABA meet ABAB, BCBC, CDCD, DADA at KK, LL, MM, NN, respectively. Compute the ratio SKLMNSABC\frac{S_{KLMN}}{S_{ABC}}
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