Geometry · Medians · Ratios along a side · Vectors · Midline

Problem 1, 2005

← Prev · 6 / 40 · Next →

CityOpen answer

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 \(CM : MB\).

A B C C₁ K M
Equal tick marks show the two midpoints: \(AC_1 = C_1B\) and \(CK = KC_1\).

Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.

Serbian Municipal Competition 2005, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source