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<CNK=? <ECD=40^o, cyclic ABCDE (2021 Novosibirsk Oral Geo Oly 9.5)

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May 25, 2021
geometrypentagonangles

Problem Statement

The pentagon ABCDEABCDE is inscribed in the circle. Line segments ACAC and BDBD intersect at point KK. Line segment CECE touches the circumcircle of triangle ABKABK at point NN. Find the angle CNKCNK if ∠ECD=40o.\angle ECD = 40^o.
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