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Poblem 3 (1st jbmo tst), moldova

Source: 1st JBMO TST, Moldova

March 31, 2006
geometry proposedgeometry

Problem Statement

The convex polygon A1A2…A2006A_{1}A_{2}\ldots A_{2006} has opposite sides parallel (A1A2∣∣A1004A1005,…)(A_{1}A_{2}||A_{1004}A_{1005}, \ldots). Prove that the diagonals A1A1004,A2A1005,…A1003A2006A_{1}A_{1004}, A_{2}A_{1005}, \ldots A_{1003}A_{2006} are concurrent if and only if opposite sides are equal.
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