Geodesic
Equioptic Points of a Triangle
Journal for geometry and graphics, Tome 17 (2013) no. 1, pp. 21-3 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 Δ have a common radical axis r. Therefore the excircles of a triangle share up to two real points, i.e., the equioptic points of Δ 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 Δ 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.
Classification : 51M04
Mots-clés : Triangle, excircle, incircle, equioptic circle, equioptic points, center of similarity, radical axis 
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     author = {B. Odehnal },
     title = {Equioptic {Points} of a {Triangle}},
     journal = {Journal for geometry and graphics},
     pages = {21--3},
     year = {2013},
     volume = {17},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2013_17_1_JGG_2013_17_1_a2/}
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B. Odehnal . Equioptic Points of a Triangle. Journal for geometry and graphics, Tome 17 (2013) no. 1, pp. 21-3. http://geodesic.mathdoc.fr/item/JGG_2013_17_1_JGG_2013_17_1_a2/