% Triangle inequality
% Copyright (c) Christian Obrecht 2004

box(-6,-9,12,10)
A C B triangle
AB = line(A,B) ; BC = line(B,C) ; CA = line(C,A)
a = distance(B,C) ; b = distance(C,A) ; c = distance(A,B)
P = point(AB,a+c) ; M = point(CA,b-a-c)
N = point(BC,a+b) ; O = point(AB,c-a-b)
R = point(CA,b+c) ; S = point(BC,a-b-c)
draw(AB) ; draw(BC) ; draw(CA)
mark(segment(A,B),simple) ; mark(segment(A,R),simple)
mark(segment(B,C),double) ; mark(segment(B,P),double)
mark(segment(C,A),cross) ; mark(segment(C,N),cross)
thickness(.5)
draw(circle(B,a),angle(BC):,angle(AB):,dashed)
draw(circle(A,a+c),angle(-CA):,angle(AB):,dashed)
draw(circle(C,b),angle(CA):,angle(BC):,dashed)
draw(circle(B,a+b),angle(-AB):,angle(BC):,dashed)
draw(circle(A,c),angle(AB):,angle(CA):,dashed)
draw(circle(C,b+c),angle(-BC):,angle(CA):,dashed)
thickness(3) ; draw(A,B,C)
draw("A",A,.5,-150:) ; draw("B",B,.4,95:)
draw("C",C,.6,-25:)
draw("M",M,-45:) ; draw("P",P,90:)
draw("N",N,0:) ; draw("O",O,-90:)
draw("R",R,-135:) ; draw("S",S,90:)
draw("$AC\le AB+BC$",point(4,3),0:)
draw("$BA\le BC+CA$",point(2,-2),0:)
draw("$CB\le BA+AC$",point(-3,2),0:)