Triangles BKM and AKD are similar in two angles, since the angle BKM = AKM as vertical angles at the intersection of straight lines AM and BD, the angle BMK = KAD as criss-crossing angles at the intersection of parallel lines BC and BD secant AM.
Since, on the condition, BM = CM = BC / 2, the coefficient of similarity of triangles is equal to:
K = BM / AD = 1/2.
Then BK / DK = 1/2.
BK + DK = BD.
DK = BK * 2.
BK + BK * 2 = BD.
3 * BK = BD.
BK = BD / 3 = 12/3 = 4 cm.
Answer: The length of the segment BK is 4 cm.
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