Tangential Triangles

In geometry, the tangential triangle of a triangle $ABC$ (other than a right triangle) is the triangle whose sides are on the tangent lines to $\triangle ABC$'s circumcircle at its vertices. Thus the incircle of the tangential triangle coincides with the circumcircle of $\triangle ABC$.

Note: A right triangle has no tangential triangle because the tangent lines to its circumcircle at its acute vertices are parallel, hence it cannot form the sides of a triangle.

• The reference triangle is the tangential triangle's contact triangle or Gergonne triangle.

• Triangle Incenter
• Circumcircle