MathDB
[KLMN]/[ABCD]<8/27

Source: Turkey TST 2003 - P2

April 6, 2013
limitinequalitiesgeometry proposedgeometry

Problem Statement

Let KK be the intersection of the diagonals of a convex quadrilateral ABCDABCD. Let L[AD]L\in [AD], M[AC]M \in [AC], N[BC]N \in [BC] such that KLABKL\parallel AB, LMDCLM\parallel DC, MNABMN\parallel AB. Show that Area(KLMN)Area(ABCD)<827.\dfrac{Area(KLMN)}{Area(ABCD)} < \dfrac {8}{27}.