In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.
Schoute's Theorem
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References
Gallatly, W. The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, p. 73, 1913.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 297-299, 1929.Schoute, P. H. Proc. Amsterdam Acad., 39-62, 1887-1888.Referenced on Wolfram|Alpha
Schoute's TheoremCite this as:
Weisstein, Eric W. "Schoute's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchoutesTheorem.html