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ABCD is cyclic implies CFIJ is cyclic

Source: Czech-Polish-Slovak 2012, P3

April 12, 2013
geometrycircumcirclecyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with circumcircle ω\omega. Let I,JI, J and KK be the incentres of the triangles ABC,ACDABC, ACD and ABDABD respectively. Let EE be the midpoint of the arc DBDB of circle ω\omega containing the point AA. The line EKEK intersects again the circle ω\omega at point FF (F≠E)(F \neq E). Prove that the points C,F,I,JC, F, I, J lie on a circle.
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