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Perpendicular if and only if Centre

Source: Pan African 2004

October 4, 2005
geometrycircumcirclecyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral such that ABAB is a diameter of it's circumcircle. Suppose that ABAB and CDCD intersect at II, ADAD and BCBC at JJ, ACAC and BDBD at KK, and let NN be a point on ABAB. Show that IKIK is perpendicular to JNJN if and only if NN is the midpoint of ABAB.
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