Geometry Problem 1116: Right Triangle, Angle Trisection, 90 Degrees, Perpendicular Lines. Level: High School, SAT Prep, Honors Geometry, College, Math Education

The figure below shows a right triangle ABC with AA₁ and AA₂ trisectors of angle BAC, similarly CC₁ and CC₂ trisectors of angle ACB. AA₁ meets CC₂ and CC₁ at C₃ and B₁, respectively. AA₂ meets CC₂ and CC₁ at B₂ and A₃, respectively. If B₁B₂ meets AC at B₃, prove that angle A₃B₃C₃ = 90 degrees.