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

mAB^{2} + nAC^{2}
= mBD^{2} + nDC^{2}
+ (m + n)AD^{2}

**Proof:**

. . . . . . add an image here, as well as a proof.

### Internet references

Wikipedia:
Apollonius' theorem

### Related pages in this website:

Summary of geometrical theorems

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