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Lines intersecting on the circumcircle (BxMO 2023, Problem 3)

Source: BxMO 2023, Problem 3

May 6, 2023
BxMOgeometry

Problem Statement

Let ABCABC be a triangle with incentre II and circumcircle ω\omega. Let NN denote the second point of intersection of line AIAI and ω\omega. The line through II perpendicular to AIAI intersects line BCBC, segment [AB][AB], and segment [AC][AC] at the points DD, EE, and FF, respectively. The circumcircle of triangle AEFAEF meets ω\omega again at PP, and lines PNPN and BCBC intersect at QQ. Prove that lines IQIQ and DNDN intersect on ω\omega.
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