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In triangle geometry, the Steiner point is a particular point associated with a plane triangle. It is a triangle center and it is designated as the center X(99) in Clark Kimberling's Encyclopedia of Triangle Centers. Jakob Steiner (1796 – 1863), Swiss mathematician, described this point in 1826. The point was given Steiner's name by Joseph Neuberg in 1886.〔 ==Definition== The Steiner point is defined as follows. (This is not the way in which Steiner defined it.〔) :Let ''ABC'' be any given triangle. Let ''O'' be the circumcenter and ''K'' be the symmedian point of triangle ''ABC''. The circle with ''OK'' as diameter is the Brocard circle of triangle ''ABC''. The line through ''O'' perpendicular to the line ''BC'' intersects the Brocard circle at another point ''A' ''. The line through ''O'' perpendicular to the line ''CA'' intersects the Brocard circle at another point ''B' ''. The line through ''O'' perpendicular to the line ''AB'' intersects the Brocard circle at another point ''C' ''. (The triangle ''A'B'C' '' is the Brocard triangle of triangle ''ABC''.) Let ''LA'' be the line through ''A'' parallel to the line ''B'C' '', ''LB'' be the line through ''B'' parallel to the line ''C'A' '' and ''LC'' be the line through ''C'' parallel to the line ''A'B' ''. Then the three lines ''LA'', ''LB'' and ''LC'' are concurrent. The point of concurrency is the ''Steiner point'' of triangle ''ABC''. In the Encyclopedia of Triangle Centers the Steiner point is defined as follows; :Let ''ABC'' be any given triangle. Let ''O'' be the circumcenter and ''K'' be the symmedian point of triangle ''ABC''. Let ''lA'' be the reflection of the line ''OK'' in the line ''BC'', ''lB'' be the reflection of the line ''OK'' in the line ''CA'' and ''lC'' be the reflection of the line ''OK'' in the line ''AB''. Let the lines ''lB'' and ''lC'' intersect at ''A″'', the lines ''lC'' and ''lA'' intersect at ''B″'' and the lines ''lA'' and ''lB'' intersect at ''C″''. Then the lines ''AA″'', ''BB″'' and ''CC″'' are concurrent. The point of concurrency is the Steiner 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）』 ■ウィキペディアで「Steiner point (triangle)」の詳細全文を読む スポンサード リンク
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