Math: Geometry Problem 1024, Art 01: Contact, Gergonne Triangle, Point on an arc of Incircle, Perpendicular, Distances. Level: School, College.

In the figure below, P is a point on the arc T_AT_C of the incircle of triangle ABC and T_AT_BT_C is the contact triangle. If PA₁, PB₁, and PC₁ 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