MathDB
Hexagon

Source: INMO 2002 Problem 1

October 10, 2005
geometrygeometric transformationreflectiongeometry solved

Problem Statement

For a convex hexagon ABCDEF ABCDEF in which each pair of opposite sides is unequal, consider the following statements.
(a1 a_1) AB AB is parallel to DE DE. (a2 a_2) AE \equal{} BD.
(b1 b_1) BC BC is parallel to EF EF. (b2 b_2) BF \equal{} CE.
(c1 c_1) CD CD is parallel to FA FA. (c2 c_2) CA \equal{} DF.
(a) (a) Show that if all six of these statements are true then the hexagon is cyclic.
(b) (b) Prove that, in fact, five of the six statements suffice.
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