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Median of a triangle

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A median of a triangle is a cevian of the triangle that joins one vertex to the midpoint of the opposite side.

In the following figure, AM is a median of triangle ABC.

Image:median.PNG

Each triangle has 3 medians. The medians are concurrent at the centroid. The centroid divides the medians (segments) in a 2:1 ratio.

Stewart's Theorem applied to the case m=n, gives the length of the median to side BC equal to
\frac 12 \sqrt{2AB^2+2AC^2-BC^2}
This formula is particularly useful when \angle CAB is right, as by the Pythagorean Theorem we find that BM=AM=CM.

See Also

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Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
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