Definition Steiner point (triangle)

the line through parallel b c , line through b parallel c , , line through c parallel b concur @ steiner point.

the steiner point defined follows. (this not way in steiner defined it.)

let abc given triangle. let o circumcenter , k symmedian point of triangle abc. circle ok diameter brocard circle of triangle abc. line through o perpendicular line bc intersects brocard circle @ point . line through o perpendicular line ca intersects brocard circle @ point b . line through o perpendicular line ab intersects brocard circle @ point c . (the triangle b c brocard triangle of triangle abc.) let la line through parallel line b c , lb line through b parallel line c , lc line through c parallel line b . 3 lines la, lb , lc concurrent. point of concurrency steiner point of triangle abc.

in encyclopedia of triangle centers steiner point defined follows;

alternative construction of steiner point



let abc given triangle. let o circumcenter , k symmedian point of triangle abc. let la reflection of line ok in line bc, lb reflection of line ok in line ca , lc reflection of line ok in line ab. let lines lb , lc intersect @ a″, lines lc , la intersect @ b″ , lines la , lb intersect @ c″. lines aa″, bb″ , cc″ concurrent. point of concurrency steiner point of triangle abc.




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