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Quadrilateral Diagonals

Source: 2019 AIME I #6

March 14, 2019
AMCAIMEAIME I2019 AIME I2019 AMCgeometryquadrilateral

Problem Statement

In convex quadrilateral KLMNKLMN side MN‾\overline{MN} is perpendicular to diagonal KM‾\overline{KM}, side KL‾\overline{KL} is perpendicular to diagonal LN‾\overline{LN}, MN=65MN = 65, and KL=28KL = 28. The line through LL perpendicular to side KN‾\overline{KN} intersects diagonal KM‾\overline{KM} at OO with KO=8KO = 8. Find MOMO.
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