# **************************************************************************
# File: Pentagon, only one solution
# ***************************************************************************


# Domains
var X1 >= -1.0e8, <= 1.0e8;
var X2 >= -1.0e8, <= 1.0e8;
var X3 >= -1.0e8, <= 1.0e8;
var X4 >= -1.0e8, <= 1.0e8;
var X5 >= -1.0e8, <= 1.0e8;
var Y1 >= -1.0e8, <= 1.0e8;
var Y2 >= -1.0e8, <= 1.0e8;
var Y3 >= -1.0e8, <= 1.0e8;
var Y4 >= -1.0e8, <= 1.0e8;
var Y5 >= -1.0e8, <= 1.0e8;
var D >= 0.3, <= 10000;


subject to
cons1 : X1^2 + Y1^2 = 1;
cons2 : X2^2 + Y2^2 = 1;
cons3 : X3^2 + Y3^2 = 1;
cons4 : X4^2 + Y4^2 = 1;
cons5 : X5^2 + Y5^2 = 1;


cons6 : (X1-X2)^2 + (Y1-Y2)^2 = D^2;
cons7 : (X2-X3)^2 + (Y2-Y3)^2 = D^2;
cons8 : (X3-X4)^2 + (Y3-Y4)^2 = D^2;
cons9 : (X4-X5)^2 + (Y4-Y5)^2 = D^2;
cons10 : (X5-X1)^2 + (Y5-Y1)^2 = D^2;

cons11 : Y1=0;
cons12 : X1=1;
cons13 : Y2 <= Y1;
cons14 : X3 <= X2;
cons15 : Y4 >= Y3;
cons16 : X5 >= X4;
cons17 : Y5 >= Y1;

solve;
display D, X1, X2, X3, X4, X5, Y1, Y2, Y3, Y4, Y5;