Steiner line
Steiner line
Let be a triangle with orthocenter is a point on the circumcircle of Then, the reflections of in three edges and point lie on a line which is known as the Steiner line of point with respect to
Collings Clime
Let triangle be the triangle with the orthocenter and circumcircle Denote any line containing point
Let and be the reflections of in the edges and respectively.
Prove that lines and are concurrent and the point of concurrence lies on
Proof
Let and be the crosspoints of with and respectively.
WLOG Let and be the points symmetric to with respect and respectively.
Therefore
Let be the crosspoint of and is cyclic
Similarly is cyclic the crosspoint of and is point
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