The perspectrix 
of a pair of paralogic
triangles 
and 
bisects the line joining the two orthocenters 
and 
(Johnson 1929, p. 259).
Sondat's Theorem
See also
Orthocenter, Paralogic Triangles, PerspectrixExplore with Wolfram|Alpha
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.Simon, M. Über die Entwicklung der Elementargeometrie im XIX. Jahrhundert. Leipzig: Teubner, 1906.Referenced on Wolfram|Alpha
Sondat's TheoremCite this as:
Weisstein, Eric W. "Sondat's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SondatsTheorem.html