The figure shows a complete quadrilateral
ABCDEF. If r_{a}, and r_{d} are the exradii of triangles
ABE and ADF, and r_{b}, and r_{c} are the inradii of
triangles BCF and CDE, prove that
.
Complete quadrilateral ABCDEF is the figure
determined by four lines, no three of which are concurrent, and their
six points of intersection A, B, C, D, E, and F. Exradius is the radius
of an excircle. Excircle is the circle tangent to the extension of two
sides and to the other side,
Inradius is the radius of an incircle. Incircle is the circle tangent to
each of the triangle's three sides.
