Geodesic
On two triangles with common side
Matematičeskoe obrazovanie, Tome 80 (2016) no. 4, pp. 15-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

Proved in the paper that when two triangles have a common side, the distance between the centers of the inscribed circles smaller than the distance between the vertices that do not lie at their common side.
Keywords: Two triangles with a common side, center of the inscribed circle. 
@article{MO_2016_80_4_a1,
     author = {B. Yamrom},
     title = {On two triangles with common side},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {15--19},
     publisher = {mathdoc},
     volume = {80},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2016_80_4_a1/}
}
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B. Yamrom. On two triangles with common side. Matematičeskoe obrazovanie, Tome 80 (2016) no. 4, pp. 15-19. http://geodesic.mathdoc.fr/item/MO_2016_80_4_a1/