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A circular horn triangle has all internal angles equal to zero. [1] One way of forming some of these triangles is to place three circles, externally tangent to each other in pairs; then the central triangular region surrounded by these circles is a horn triangle.
An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides, and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
A circle that is tangent to two sides of a triangle, as the Malfatti circles are, must be centered on one of the angle bisectors of the triangle (green in the figure). These bisectors partition the triangle into three smaller triangles, and Steiner's construction of the Malfatti circles begins by drawing a different triple of circles (shown ...
Printable version; In other projects Wikidata item; Appearance. ... Help. Pages in category "Circles defined for a triangle" The following 15 pages are in this ...
When the outer Soddy circle has positive curvature, both Soddy centers are equal detour points. When the outer Soddy circle has negative curvature, its center is the isoperimetric point: the triangles ABP 2, BCP 2, and CAP 2 have equal perimeter. In geometry, the Soddy circles of a triangle are two circles associated with any triangle in the
In plane geometry, a mixtilinear incircle of a triangle is a circle which is tangent to two of its sides and internally tangent to its circumcircle. The mixtilinear incircle of a triangle tangent to the two sides containing vertex A {\displaystyle A} is called the A {\displaystyle A} -mixtilinear incircle.