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
. . . . . . add an image here, as well as a proof.
Wikipedia: Apollonius' theorem
Summary of geometrical theorems
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