Unformatted text preview: BC = DA and BC not parallel with DA . Let two variable points E and F lie of the sides BC and DA , respectively and satisfy BE = DF . The lines AC and BD meet at P , the lines BD and EF meet at Q , the lines EF and AC meet at R . Prove that the circumcircles of the triangles PQR , as E and F vary, have a common point other than P . Problem 6 . In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2 5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each. 1...
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 Fall '11
 T.S.
 Natural number, Prime number, Euclidean algorithm, A1 A2 B1

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