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[parent] lengths of triangle medians (Corollary)

By the Apollonius theorem, in any triangle, the lengths $m_a$ $m_b$ $m_c$ of the medians of opposing the the sides $a$ $b$ $c$ respectively, are $$m_a = \frac{1}{2}\sqrt{2b^2+2c^2-a^2},$$ $$m_b = \frac{1}{2}\sqrt{2c^2+2a^2-b^2},$$ $$m_c = \frac{1}{2}\sqrt{2a^2+2b^2-c^2}.$$




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See Also: proof of Apollonius theorem, common point of triangle medians, lengths of angle bisectors

Other names:  lengths of medians

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Cross-references: sides, triangle, Apollonius theorem

This is version 2 of lengths of triangle medians, born on 2008-09-29, modified 2008-09-29.
Object id is 11107, canonical name is LengthsOfTriangleMedians.
Accessed 754 times total.

Classification:
AMS MSC51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)

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