Equioptic Points of a Triangle

The locus of points where two non-concentric circles c1 and c2 are seen under equal angles is the equioptic circle e. The equioptic circles of the excircles of a triangle ∆ have a common radical axis r. Therefore the excircles of a triangle share up to two real points, i.e., the equioptic points of ∆ from which the circles can be seen under equal angles. The line r carries a lot of known triangle centers. Further we find that any triplet of circles tangent to the sides of ∆ has up to two real equioptic points. The three radical axes of triplets of circles containing the incircle are concurrent in a new triangle center.