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AK+BM=CM in rectangle, CK=BC (2017 Novosibirsk Oral Geo Oly 8-9 p5)

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April 26, 2021
geometryrectangleequal segments

Problem Statement

Point KK is marked on the diagonal ACAC in rectangle ABCDABCD so that CK=BCCK = BC. On the side BCBC, point MM is marked so that KM=CMKM = CM. Prove that AK+BM=CMAK + BM = CM.
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