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AN = 2KM if AK = BK - All-Russian MO 1993 Regional (R4) 10.1

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August 26, 2024
geometryequal segments

Problem Statement

Point DD is chosen on the side ACAC of an acute-angled triangle ABCABC. The median AMAM intersects the altitude CHCH and the segment BDBD at points NN and KK respectively. Prove that if AK=BKAK = BK, then AN=2KMAN = 2KM.
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