In the figure below,
ABC is an isosceles triangle (AB = BC) D is a point on AC, r_{1}
and r_{2} are the exradii of the triangle ABD corresponding to AB
and AD, respectively; r_{3} and r_{4} are the exradii of the triangle
DBC corresponding to BC and CD, respectively. Prove that r_{1} + r_{2}
= r_{3} + r_{4}.

*BD is called an interior
cevian of triangle ABC. *

See also:

Art of problem 1377.