The figure shows a right triangle ABC with the angle bisector BQ and
the external squares ABDE and BCFG. AF meets BC at M and CE
meets AB at N. ED and FG meet at H, EA and FC meet at P. Prove
that area ABC (S) is one-half of the geometric mean of areas EHFP (S_{1})
and BMQN (S_{2}) that is
.