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. Prove that (1) AC_{1}
= AB_{2}, similarly CA_{1}
= CB_{2}; (2) B_{2}C_{1}
= B_{2}A_{1}.
