Geodesic
A Triad of Circles Externally Tangent to the Nine-Point Circle and Internally Tangent to Two Sides of a Triangle
Journal for geometry and graphics, Tome 18 (2014) no. 1, pp. 61-71.

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We determine the three circles in the interior of an acute triangle Δ which touch the nine-point circle n from the outside and two sides of Δ from the inside. Some perspective triangles related to Δ and the three circles are found. A more general result on tangent triangles related to Apollonian configurations of circles leads to a specific result in the case of a special Apollonian configuration derived from the three circles in question. All constructions are linear once the excircles of the base triangle are constructed.
Classification : 51N20
Mots-clés : Triangle, nine-point circle, Apollonian problem, tangent triangle, perspective triangles 
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     title = {A {Triad} of {Circles} {Externally} {Tangent} to the {Nine-Point} {Circle} and {Internally} {Tangent} to {Two} {Sides} of a {Triangle}},
     journal = {Journal for geometry and graphics},
     pages = {61--71},
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B. Odehnal . A Triad of Circles Externally Tangent to the Nine-Point Circle and Internally Tangent to Two Sides of a Triangle. Journal for geometry and graphics, Tome 18 (2014) no. 1, pp. 61-71. http://geodesic.mathdoc.fr/item/JGG_2014_18_1_JGG_2014_18_1_a4/