% This figure was an illustration for an exercice about
% perpendicular bisectors.
% Copyright (c) Christian Obrecht 2001

frame(-3.5,-3.5,3.5,3.5)

O = point(0,0) ; c = circle(O,3)
A = point(c,135:) ; B = point(c,45:)
C = point(c,-30:) ; D = point(c,-110:)
I = barycenter(A,B) ; J = barycenter(B,C)
K = barycenter(C,D) ; L = barycenter(D,A)
P = projection(I,line(C,D))
Q = projection(J,line(D,A))
R = projection(K,line(A,B))
S = projection(L,line(B,C))

tricks "psset{linearc=.5pt}"
draw(A,B,C,D) ; draw(c)
draw("$F$",A,.2,135:) ; draw("$B$",B,.2,45:)
draw("$C$",C,.2,-30:) ; draw("$D$",D,.2,-120:)
draw(O,plus) ; draw("$O$",O,.15,90:)

color(gray)
draw("$I$",I,.2,90:) ; draw("$J$",J,.2,15:)
draw("$K$",K,.2,-90:) ; draw("$L$",L,.2,180:)
draw(segment(I,P)) ; draw(segment(J,Q))
draw(segment(K,R)) ; draw(segment(L,S))
mark(I,R,K,right) ; mark(L,S,C,right)
mark(I,P,D,right) ; mark(D,Q,J,right)