At the points where a line 
cuts the sides of a triangle 
, draw three perpendiculars
to the sides, one through each point of intersection. The resulting three lines intersect
pairwise in three points that form a triangle 
known as the paralogic triangle of 
. The paralogic and original triangles are similar triangles, and two triangles are also perspective triangles with the line 
being the perspectrix.
Amazingly, the circumcircles of 
and 
meet orthogonally
in two points, with one point of intersection being their similitude
center, and the other being their perspector (Johnson
1929, p. 258).
