Tangential Triangle

The Triangle $\Delta T_1T_2T_3$ formed by the lines tangent to the Circumcircle of a given Triangle $\Delta A_1A_2A_3$ at its Vertices. It is the Pedal Triangle of $\Delta A_1A_2A_3$ with the Circumcenter as the Pedal Point. The Trilinear Coordinates of the Vertices of the tangential triangle are

$$A' = -a:b:c$$

$$B' = a:-b:c$$

$$C' = a:b:-c.$$

The Contact Triangle and tangential triangle are perspective from the Gergonne Point.

See also Circumcircle, Contact Triangle, Gergonne Point, Pedal Triangle, Perspective