Tarry point Steiner point (triangle)

the line through perpendicular b c , line through b perpendicular c , , line through c perpendicular b concur @ tarry point.

the tarry point of triangle closely related steiner point of triangle. let abc given triangle. point on circumcircle of triangle abc diametrically opposite steiner point of triangle abc called tarry point of triangle abc. tarry point triangle center , designated center x(98) in encyclopedia of triangle centers. trilinear coordinates of tarry point given below:

( sec ( + ω ) : sec (b + ω ) : sec ( c + ω ) ),



where ω brocard angle of triangle abc.




= ( f( a, b, c ) : f( b, c, ) : f( c, a, b ) ),



where f( a, b, c ) = bc / ( b + c − ab − ac )

similar definition of steiner point, tarry point can defined follows:

let abc given triangle. let b c brocard triangle of triangle abc. let la line through perpendicular line b c , lb line through b perpendicular line c , lc line through c perpendicular line b . 3 lines la, lb , lc concurrent. point of concurrency tarry point of triangle abc.