Congruent isoscelizers point explained

In geometry, the congruent isoscelizers point is a special point associated with a plane triangle. It is a triangle center and it is listed as X(173) in Clark Kimberling's Encyclopedia of Triangle Centers. This point was introduced to the study of triangle geometry by Peter Yff in 1989.^{[1] [2]}

Definition

An isoscelizer of an angle in a triangle is a line through points and, where lies on and on, such that the triangle is an isosceles triangle. An isoscelizer of angle is a line perpendicular to the bisector of angle .

Let be any triangle. Let be the isoscelizers of the angles respectively such that they all have the same length. Then, for a unique configuration, the three isoscelizers are concurrent. The point of concurrence is the congruent isoscelizers point of triangle .^[1]

Properties

• The trilinear coordinates of the congruent isoscelizers point of triangle are^[1]

• The intouch triangle of the intouch triangle of triangle is perspective to, and the congruent isoscelizers point is the perspector. This fact can be used to locate by geometrical constructions the congruent isoscelizers point of any given .^[1]

See also

• Yff center of congruence
• Equal parallelians point

Notes and References

1. Encyclopedia: Kimberling . Clark . X(173) = Congruent isoscelizers point . Encyclopedia of Triangle Centers . 3 June 2012 . dead . https://web.archive.org/web/20120419171900/http://faculty.evansville.edu/ck6/encyclopedia/ETC.html . 19 April 2012 .
2. Web site: Kimberling. Clark. Congruent isoscelizers point. 3 June 2012.