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. If B_{1}B_{2}
meets AC at B_{3}, prove that angle A_{3}B_{3}C_{3}
= 90 degrees.
