The Gergonne triangle (of 
) is defined by the three touchpoints of the incircle on the three sides. The touchpoint opposite 
is denoted 
, etc.
) is defined by the three touchpoints of the incircle on the three sides. The touchpoint opposite is denoted , etc.
This Gergonne triangle 
, is also known as the contact triangle or intouch triangle of .
, is also known as the contact triangle or intouch triangle of . Its area is
where 
, 
, and 
are the area, radius of the incircle, and semiperimeter of the original triangle, and 
, 
, and 
are the side lengths of the original triangle. This is the same area as that of the extouch triangle.
, , and are the area, radius of the incircle, and semiperimeter of the original triangle, and , , and are the side lengths of the original triangle. This is the same area as that of the extouch triangle.
