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Congruent isoscelizers point
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Congruent isoscelizers point : ウィキペディア英語版
Congruent isoscelizers point

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.
==Definition==

An isoscelizer of an angle A in a triangle ABC is a line through points ''P''1 and ''Q''1, where ''P''1 lies on ''AB'' and ''Q''1 on ''AC'', such that the triangle ''AP''1''Q''1 is an isosceles triangle. An isoscelizer of angle A is a line perpendicular to the bisector of angle A.
Let ''ABC'' be any triangle. Let ''P''1''Q''1, ''P''2''Q''2, ''P''3''Q''3 be the isoscelizers of the angles ''A'', ''B'', ''C'' respectively such that they all have the same length. Then the three isoscelizers ''P''1''Q''1, ''P''2''Q''2, ''P''3''Q''3 are concurrent. The point of concurrence is the ''congruent isoscelizers point'' of triangle ''ABC''.〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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