The figure below shows a right triangle ABC with AA_{1}
and AA_{2}
trisectors of angle BAC, similarly CC_{1}
and CC_{2}
trisectors of angle ACB. AA_{1}
meets CC_{2}
and CC_{1}
at C_{3}
and B_{1},
respectively. AA_{2}
meets CC_{2}
and CC_{1}
at B_{2}
and A_{3}, respectively. B_{1}B_{2}
meets AC at B_{3}, B_{3}C_{3}
meets AA_{2} at A_{4}, and B_{3}A_{3} meets CC_{2} at C_{4}. Prove that A_{1}B_{2} //
B_{1}A_{4}, similarly C_{1}B_{2}
// B_{1}C_{4}.
