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Geometry Mathley 2.4 concurrency

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June 6, 2020
geometryconcurrentincentercircumcircle

Problem Statement

Let ABCABC be a triangle inscribed in a circle of radius OO. The angle bisectors AD,BE,CFAD,BE,CF are concurrent at II. The points M,N,PM,N, P are respectively on EF,FDEF, FD, and DEDE such that IM,IN,IPIM, IN, IP are perpendicular to BC,CA,ABBC,CA,AB respectively. Prove that the three lines AM,BN,CPAM,BN, CP are concurrent at a point on OIOI.
Nguyễn Minh Hà
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