# Tangential Triangles

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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.

#### Contents

## Properties

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

## See Also

**Cite as:**Tangential Triangles.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/tangential-triangles/