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BC=KM if CM=CK and <CBM = 2 <ABM and K lies on median BM

Source: 2021 Saudi Arabia JBMO TST 2.2

September 4, 2021
geometryequal segmentsequal angles

Problem Statement

In a triangle ABCABC, let KK be a point on the median BMBM such that CM=CKCM = CK. It turned out that ∠CBM=2∠ABM\angle CBM = 2\angle ABM. Show that BC=KMBC = KM.
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