Frank M. Jackson and Stalislav Takhaev, Heronian triangles of class K: congruent incircles cevian perspective,
Forum Geometricorum, 15 (2015) 5--12.
Abstract. We relate the properties of a cevian that divides a reference triangle into two sub-triangles with congruent incircles to the system of inner and outer Soddy circles of the same reference triangle. We show that if constraints are placed on the reference triangle then relationships exist between the Soddy circles, the incircle of the reference triangle and the congruent incircles of the sub-triangles. In particular, we show that a class of Heronian triangles exists with inradius equal to integer multiples of their inner and outer Soddy circle radii.
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