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right angle inside a rectangle wanted (HOMC 2018 Ind. p12)

Source:

January 31, 2020
geometryrectangle

Problem Statement

Let ABCD be a rectangle with 45o<∠ADB<60o45^o < \angle ADB < 60^o. The diagonals ACAC andBD BD intersect at OO. A line passing through OO and perpendicular to BDBD meets ADAD and CDCD at MM and NN respectively. Let KK be a point on side BCBC such that MK∥ACMK \parallel AC. Show that ∠MKN=90o\angle MKN = 90^o. https://cdn.artofproblemsolving.com/attachments/4/1/1d37b96cebaea3409ade7ce6711ac2d3fc2ef9.png
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