The figure below shows a triangle ABC of sides a, b, c
with the cevians BM and BN so that the angles A and C are congruent to the
angles NBC and ABM, respectively. BM = d, BN = d1, AM = m, and CN = n.
Prove that (1) triangle MBN is isosceles: d = d1; (2) triangles AMB , BNC and ABC are similar; (3) a2
= b.n, similarly c2 = b.m; (4) d2 = m.n; (5) a2 + c2 = b.(m+n) Qurra's
theorem; (6) 1/a2 + 1/c2