Catriona's Circle in a Triangle

Catriona Agg (neƩ Shearer) shared this sweet little puzzle: what is the area of a circle inscribed in a 13, 14, 15 triangle. https://twitter.com/Cshearer41/status/1299281163228516352?s=20[br][br]Such an elegant observation, I thought we might want to look for more.

Information: Catriona's Circle in a Triangle