section_path: Inscription in or circumscription about other figures
section_name: Inscription in or circumscription about other figures
paragraph_text: Inscription in or circumscription about other figures
  
  In every triangle a unique circle, called the incircle, can be inscribed such that it is tangent to each of the three sides of the triangle.
  
  About every triangle a unique circle, called the circumcircle, can be circumscribed such that it goes through each of the triangle's three vertices.
  
  A tangential polygon, such as a tangential quadrilateral, is any convex polygon within which a circle can be inscribed that is tangent to each side of the polygon. Every regular polygon and every triangle is a tangential polygon.
  
  A cyclic polygon is any convex polygon about which a circle can be circumscribed, passing through each vertex. A well-studied example is the cyclic quadrilateral. Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called a bicentric polygon.
  
  A hypocycloid is a curve that is inscribed in a given circle by tracing a fixed point on a smaller circle that rolls within and tangent to the given circle.