Stewart's Theorem
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[hide]Statement
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If a cevian of length t is drawn and divides side a into segments m and n, then
Proof
For this proof we will use the law of cosines and the identity .
Label the triangle with a cevian extending from onto , label that point . Let CA = n Let DB = m. Let AD = t. We can write two equations:
When we write everything in terms of cos(CDA) we have:
Now we set the two equal and arrive at Stewart's theorem:
Example
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