07-03-2026, 04:45 PM
Hart circle
Summary
The Hart circle is a concept from advanced circle geometry where three mutually intersecting circles form a network of eight “circular triangles.” For each of these configurations, there exists a special circle that is tangent to the incircles of a chosen triangle and its neighboring triangles, and this circle is called a Hart circle.
Remarkably, a single set of three circles gives rise to eight such Hart circles, each tied to a different choice of base triangle. Geometers often view it as a curved analogue of the nine-point circle from classical triangle geometry, extending familiar ideas about tangency and symmetry into a more complex circular setting.
ARTICLE
Summary
The Hart circle is a concept from advanced circle geometry where three mutually intersecting circles form a network of eight “circular triangles.” For each of these configurations, there exists a special circle that is tangent to the incircles of a chosen triangle and its neighboring triangles, and this circle is called a Hart circle.
Remarkably, a single set of three circles gives rise to eight such Hart circles, each tied to a different choice of base triangle. Geometers often view it as a curved analogue of the nine-point circle from classical triangle geometry, extending familiar ideas about tangency and symmetry into a more complex circular setting.
ARTICLE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘