The figure shows a triangle ABC with obtuse angle A,
the orthocenter H, the circumradius R, the inradius r,
and the exradii, r_{a}, r_{b}, and r_{c}.
If AH = a_{1}, BH = b_{1}, and CH = c_{1}, prove
that r_{a} + r_{b} + r_{c} + r =  a_{1}
+ b_{1} + c_{1} + 2R.
