Apollonius' Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The theorem can be proved as a special case of Stewart''s theorem, or can be proved using vectors (see parallelogram law). The following is an independent proof using the law of cosines. Let the triangle have sides a, b, c with a median d drawn to side a. Let m be the length of the segments of a formed by the median, so m is half of a. Let the angles formed between a and d be and where includes b and includes c. Then is the supplement of and cos = cos .
