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Cyclic quadrilateral with midpoints of arcs;-[INMO 2011]

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February 6, 2011
geometrycyclic quadrilateralgeometry unsolved

Problem Statement

Let ABCDABCD be a cyclic quadrilateral inscribed in a circle Γ.\Gamma. Let E,F,G,HE,F,G,H be the midpoints of arcs AB,BC,CD,ADAB,BC,CD,AD of Γ,\Gamma, respectively. Suppose that AC⋅BD=EG⋅FH.AC\cdot BD=EG\cdot FH. Show that AC,BD,EG,FHAC,BD,EG,FH are all concurrent.
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