equal incircles theorem | inscribed circle

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the radius r of the circle is called the inradius. An incircle of a polygon is the two-dimensional case of an insphere of a solid. While an incircle does not necessarily exist for arbitrary polygons, it exists and is moreover unique for triangles, regular polygons, and some other polygons including rhombi, bicentric polygons, and tangential quadrilaterals.

circumcircle | congruent incircles | congruent incircles point | contact triangle | excircles | incenter | incentral triangle | inradius | insphere | Japanese theorem | seven circles theorem | tangent circles | tangential triangle | triangle transformation principle