The following theorem has been attributed to Apollonius: In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side.

See complete illustration at:

gogeometry.com/geometry/median_length_apollonius_theorem.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Thursday, February 12, 2009

### Median length, Apollonius' Theorem

Labels:
Apollonius,
median,
triangle

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