KPV See also Triangle Madness for a whizzlet showing the

**circumcenter**of a triangle plus some other interesting points such as the

**incenter**,

**centroid**,

**orthocenter**, etc.

# circumcenter.tcl # Quick demo program about finding the circumcenter of three # points. E.g. given three points, find the center of the # circle which passes through all three points. Derived from # the book "A Programmer's Geometry". --willdye, 2004-11-23 set Kx 80.0 ; set Ky 50.0 ;# First point set Lx 200.0 ; set Ly 20.0 ;# Second point set Mx 230.0 ; set My 100.0 ;# Third point set LKx [expr { $Lx - $Kx }] ; set LKy [expr { $Ly - $Ky }] set MKx [expr { $Mx - $Kx }] ; set MKy [expr { $My - $Ky }] set faccuracy 0.00001 ;# Value depends on the application. set determinant [expr { $LKx * $MKy - $MKx * $LKy }] if {[expr { abs( $determinant ) < $faccuracy }]} { puts "Error: two or more points are coincident." ; exit} set d2 [expr { 0.5 / $determinant }] set LKr [expr { $LKx * $LKx + $LKy * $LKy }] set MKr [expr { $MKx * $MKx + $MKy * $MKy }] set Cx [expr {( $LKr * $MKy - $MKr * $LKy ) * $d2 + $Kx }] set Cy [expr {( $LKx * $MKr - $MKx * $LKr ) * $d2 + $Ky }] # We'll probably want the radius, also. The straightforward # method should be good enough in this case, but of course in # general it is not very efficent, and has some accuracy issues. set rad [expr { sqrt( pow( ( $Cx - $Kx ), 2 ) + pow( ( $Cy - $Ky ), 2 ) ) }] # Display the result. puts "Circumcenter, as X/Y/Radius: $Cx $Cy $rad" if {![package present Tk]} {exit} destroy .c ; canvas .c -background gray ; pack .c .c create polygon $Lx $Ly $Mx $My $Kx $Ky -fill white .c create oval $Cx $Cy $Cx $Cy -fill black .c create oval [expr { $Cx - $rad }] [expr { $Cy - $rad }] \ [expr { $Cx + $rad }] [expr { $Cy + $rad }] -outline red

uniquename 2013aug18Here is an image of what is drawn on the canvas, by the code above. (I replaced a 'puts' statement by a statement to put the x,y,radius data on the canvas, instead of to 'stdout'.)