Apollonius' theorem states that given a triangle ABC, if D is any point on BC such that it divides BC in the ratio n:m (or mBD = nDC), then

mAB² + nAC² = mBD² + nDC² + (m + n)AD²

Proof:

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Internet references

Wikipedia: Apollonius' theorem

Related pages in this website:

Summary of geometrical theorems

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