The figure shows a right triangle ACB,
BH is the altitude drawn to the hypotenuse, HE is perpendicular
to BC, HF is perpendicular to AC, and EM and FN are
perpendicular to AB. If BC = a, AC = b,
AB = c, and CH = h, prove that
(5) HM = HN, and (6)
twice the geometric mean of AN and BM.