If 
is any point on a line 
whose orthopole is 
, then the circle power of
with respect to the pedal
circle of 
is a constant (Gallatly 1913, p. 51).
Lemoyne's Theorem
See also
Circle Power, Orthopole, Pedal CircleExplore with Wolfram|Alpha
References
Gallatly, W. "Lemoyne's Theorem." §77 in The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, pp. 51-52, 1913.Referenced on Wolfram|Alpha
Lemoyne's TheoremCite this as:
Weisstein, Eric W. "Lemoyne's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LemoynesTheorem.html