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China Mathematical Olympiad 1986 problem4

Source: China Mathematical Olympiad 1986 problem4

January 18, 2014
geometrygeometry unsolved

Problem Statement

Given a △ABC\triangle ABC with its area equal to 11, suppose that the vertices of quadrilateral P1P2P3P4P_1P_2P_3P_4 all lie on the sides of △ABC\triangle ABC. Show that among the four triangles △P1P2P3,△P1P2P4,△P1P3P4,△P2P3P4\triangle P_1P_2P_3, \triangle P_1P_2P_4, \triangle P_1P_3P_4, \triangle P_2P_3P_4 there is at least one whose area is not larger than 1/41/4.
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