geometrypower of a pointradical axisgeometry proposed
Problem Statement
Isosceles triangles A3A1O2 and A1A2O3 are constructed on the sides of
a triangle A1A2A3 as the bases, outside the triangle. Let O1 be a point
outside ΔA1A2A3 such that
∠O1A3A2=21∠A1O3A2 and ∠O1A2A3=21∠A1O2A3.
Prove that A1O1⊥O2O3, and if T is the projection of O1 onto A2A3,
then O2O3A1O1=2A2A3O1T.