Hart’s theorem says
If a triangle be formed by the arcs of three circles, the inscribed and the three escribed circles are all tangent to a new circle or line.
Here “triangle” means a three-sided figure whose sides are portions of a circle. The inscribed circle is the largest circle that can fit inside the three-sided figure.
The “escribed” circles are analogous to the excircles in the previous post: you extend two sides and find a circle that is tangent to the triangle side and the extended side. The difference here being that the side extensions are now circles.
