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lengths of triangle medians
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(Corollary)
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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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"lengths of triangle medians" is owned by pahio.
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(view preamble | get metadata)
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 MSC: | 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries) |
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Pending Errata and Addenda
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