Let
be inscribed in a nondegenerate conic
section,
and let
be a point on neither nor any of the three side lines of
the triangle. Let , , and meet again at , , and , respectively. For a point on or on the polar of with respect to , define
(1)
(2)
(3)
Assume that the second intersections differ from the initial vertices and that all three displayed
intersections are well-defined, finite, and distinct.
Then ,
,
and
are collinear. Their line
also contains iff lies on (Tran 2018, p. 145).
Tran (2018, pp. 146-148) gives a synthetic proof
and derives several classical theorems as special cases.
be inscribed in a nondegenerate conic
section 
,
and let 
be a point on neither 
nor any of the three side lines of
the triangle. Let 
, 
, and 
meet 
again at 
, 
, and 
, respectively. For a point 
on 
or on the polar of 
with respect to 
, define
,
,
and 
are collinear. Their line
also contains 
iff 
lies on 
(Tran 2018, p. 145).
