Problem1. Let ABC be a triangle,and let D, E, F be the point softangency of
the incircle of triangle ABC with the sides BC, CA and AB respectively.Let X be
in the interior of ABC such that the incircle of XBC touches XB, XC and BC in
Z, Y and D respectively.Prove that EFZY is cyclic.
Problem2. Let ABCD be a convex quadrilateral.Let E = AB ? CD, F =
AD ?BC, P = AC ?BD,and let O the foot of the perpendicular from P to the
line EF.Prove thatBOC =AOD.
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