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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

$\displaystyle A'$ $\textstyle =$ $\displaystyle -a:b:c$  
$\displaystyle B'$ $\textstyle =$ $\displaystyle a:-b:c$  
$\displaystyle C'$ $\textstyle =$ $\displaystyle a:b:-c.$  

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

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

© 1996-9 Eric W. Weisstein