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concyclic, AB=AN+PB, BC=BP+MC, CA=CM+AN 2018 Ecuador NMO (OMEC) 3.5

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September 18, 2021
cyclic quadrilateralConcyclicequal segments

Problem Statement

Let ABCABC be an acute triangle and let MM, NN, and P P be on CBCB, ACAC, and ABAB, respectively, such that AB=AN+PBAB = AN + PB, BC=BP+MCBC = BP + MC, CA=CM+ANCA = CM + AN. Let ℓ\ell be a line in a different half plane than CC with respect to to the line ABAB such that if X,YX, Y are the projections of A,BA, B on ℓ\ell respectively, AX=APAX = AP and BY=BPBY = BP. Prove that NXYMNXYM is a cyclic quadrilateral.
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