Stewart's theorem: If a cevian AD of length d divides side BC into segments m (BD) and n (DC), then b^2m + c^2n - d^2a = am*n. For a median (m = n = a/2): the median length formula is m_a = (1/2)*sqrt(2b^2 + 2c^2 - a^2). This is occasionally tested in JEE.