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