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 reduniquename 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'.)
