Hart’s theorem

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. The post Hart’s theorem first appeared on John D. Cook.