In the figure below, P is a point on
the arc T_{A}T_{C} of the incircle of triangle ABC and T_{A}T_{B}T_{C} is the contact triangle.
If PA_{1}, PB_{1}, and PC_{1} are perpendicular to BC, AC,
and AB, respectively,
Prove that:
.
The contact triangle or intouch triangle or Gergonne triangle
of a triangle ABC is defined by the 3 tangency points of the
incircle on the 3 sides.
See
also:
Art 00
