The third pedal triangle is similar to the original one. This theorem can be generalized to: the th
pedal -gon
of any -gon
is similar to the original one. It is also true that

(6)

(Johnson 1929, pp. 135-136; Stewart 1940; Coxeter and Greitzer 1967, p. 25). The area of the pedal triangle of a point is proportional to the power of
with respect to the circumcircle,

(7)

(8)

(Johnson 1929, pp. 139-141).

The only closed billiards path of a single circuit in an acute triangle is the pedal triangle. There
are an infinite number of multiple-circuit paths, but all segments are parallel to
the sides of the pedal triangle (Wells 1991).