The figure below shows the circles O_{1}
(radius r_{1}) and O_{2} (radius r_{2}). A_{1}A_{2}
and B_{1}B_{2}
are the common
external tangents and CD is a common internal tangent. Circle O_{3}
(radius r_{3}) touches A_{1}C, CD, and circle O_{1}.
Circle O_{4} (radius r_{4}) touches B_{1}D, CD, and circle O_{1}.
Prove that
.
See also:
Art and typography of problem 1099.
