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The vertices of the convex quad ABCD are integer points

Source: P6: Bosnia and Herzegovina TST 2002

October 3, 2014
geometrygeometry unsolved

Problem Statement

The vertices of the convex quadrilateral ABCDABCD and the intersection point SS of its diagonals are integer points in the plane. Let PP be the area of ABCDABCD and P1P_1 the area of triangle ABSABS. Prove that \sqrt{P} \ge \sqrt{P_1}+\frac{\sqrt2}2
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