In a triangle ABC (figure below), the excircle E
corresponding to BC is tangent to AB, BC, and AC at C_{1},
A_{1}, and B_{1}, respectively. AB_{2}
is parallel to A_{1}B_{1} (B_{2} on C_{1}A_{1}
extended), AC_{2} is parallel to C_{1}A (C_{2} on B_{1}A_{1}
extended). B_{2}C_{2} intersects AC and AB at B_{3}
and C_{3}, respectively. Prove that B_{3}C_{3}
= BC/2.
