Geometry · Medians · Ratios along a side · Vectors · Midline
In a triangle \(ABC\), let \(C_1\) be the midpoint of the side \(AB\), so that \(CC_1\) is the median from \(C\). Let \(K\) be the midpoint of the segment \(CC_1\), and let the line \(AK\) meet the side \(BC\) at a point \(M\). Determine the ratio \(CM : MB\).
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Serbian Municipal Competition 2005, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source