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Planimetry

Source: Polish National Olympiad 2016 P2- Final Round

April 8, 2016
circumscribed quadrilateralgeometry

Problem Statement

Let ABCDABCD be a quadrilateral circumscribed on the circle ω\omega with center II. Assume ∠BAD+∠ADC<π\angle BAD+ \angle ADC <\pi. Let M, NM, \ N be points of tangency of ω\omega with AB, CDAB, \ CD respectively. Consider a point K∈MNK \in MN such that AK=AMAK=AM. Prove that IDID bisects the segment KNKN.
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