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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.
The intersection of three circular disks forms a convex circular triangle. For instance, a Reuleaux triangle is a special case of this construction where the three disks are centered on the vertices of an equilateral triangle, with radius equal to the side length of the triangle. However, not every convex circular triangle is formed as an ...
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
Print/export Download as PDF; Printable version; ... Help. Pages in category "Circles defined for a triangle" The following 15 pages are in this category, out of 15 ...
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 ...
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.