Hart’s theorem
Hart's theorem states that if a triangle is formed by the arcs of three circles, the inscribed circle and the three escribed circles are all tangent to a new circle or line.
Background
- This is a geometry theorem by Andrew Hart (mid-1800s), part of a family of results about circles tangent to other circles — a topic once central to 19th-century mathematics but now obscure to most readers.
- The post extends a classic Greek result (the incircle and excircles of a triangle) from straight-sided triangles to *curvilinear* triangles made of circular arcs. Escribed circles are circles tangent to one side of a triangle and the extensions of the other two sides.
- John D. Cook is a mathematician and blogger who writes short, accessible explanations of math and computer science for a general audience. His blog is widely followed in technical circles.