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Nice geometry

Source: Chinese TST 2007 6th quiz P2

October 12, 2007
geometrycircumcircleincentersymmetryEulerprojective geometrycyclic quadrilateral

Problem Statement

Let ABCD ABCD be the inscribed quadrilateral with the circumcircle ω \omega.Let ζ \zeta be another circle that internally tangent to ω \omega and to the lines BC BC and AD AD at points M,N M,N respectively.Let I1,I2 I_1,I_2 be the incenters of the △ABC \triangle ABC and △ABD \triangle ABD.Prove that M,I1,I2,N M,I_1,I_2,N are collinear.
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