A congruent-incircle cevian of a triangle subdivides the triangle into two triangles with congruent incircles. We give two Euclidean constructions of such cevians, and also construct Heronian triangles for which the three pairs of congruent-incircle subtriangles are all Heronian.
"The Congruent-Incircle Cevians of a Triangle." Missouri J. Math. Sci. 15 (1) 21 - 32, Winter 2003. https://doi.org/10.35834/2003/1501021