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2008 ToT Spring Junior A P2 if AK = AO and KM = MC, then AM = KB

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February 26, 2020
geometryequal segments

Problem Statement

A line parallel to the side ACAC of triangle ABCABC cuts the side ABAB at KK and the side BCBC at MM. OO is the intersection point of AMAM and CKCK. If AK=AOAK = AO and KM=MCKM = MC, prove that AM=KBAM = KB.
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