In the figure below, P is a point on
the incircle of triangle ABC and T_{A}T_{B}T_{C} is the contact triangle.
If PA_{1}, PB_{1}, PC_{1}, PA_{2}, PB_{2}, and PC_{2} are perpendicular to BC, AC,
AB, T_{B}T_{C}, T_{A}T_{C}, and
T_{A}T_{B}, respectively,
Prove that
PA_{1}.PB_{1}.PC_{1}
= PA_{2}.PB_{2}.PC_{2}.
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.
