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calculate the perimeter of triangle MNP

Source: 2024 5th OMpD L2 P2 - Brazil - Olimpíada Matemáticos por Diversão

October 16, 2024
geometryperimeter

Problem Statement

Let ABCDABCD be a convex quadrilateral, and MM, NN, and PP be the midpoints of diagonals ACAC and BDBD, and side ADAD, respectively. Also, suppose that ∠ABC+∠DCB=90\angle{ABC} + \angle{DCB} = 90 and that AB=6AB = 6, CD=8CD = 8. Calculate the perimeter of triangle MNPMNP.
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