section_path: Related figures/Figures circumscribed about a triangle
section_name: Figures circumscribed about a triangle
paragraph_text: Figures circumscribed about a triangle
  
  The tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices.
  
  As mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the perpendicular bisectors of the triangle's sides. Furthermore, every triangle has a unique Steiner circumellipse, which passes through the triangle's vertices and has its center at the triangle's centroid. Of all ellipses going through the triangle's vertices, it has the smallest area.
  
  The Kiepert hyperbola is the unique conic that passes through the triangle's three vertices, its centroid, and its circumcenter.
  
  Of all triangles contained in a given convex polygon, one with maximal area can be found in linear time; its vertices may be chosen as three of the vertices of the given polygon.