#include <stdio.h>
#include <stdlib.h>
#include <math.h>

void prettyprint ( double A, double B, double C )
{
   if (A == 0) {
      printf("%lf y", B);
   } else {
      printf("%lf x", A);
      if (B > 0) printf(" + %lf y", B);
      else if (B < 0) printf(" - %lf y", -B);
   }
   if (C > 0) printf(" + %lf", C);
   else if (C < 0) printf(" - %lf", -C);
   printf(" = 0\n");
}

int main ()
{
   double Ax, Ay, Bx, By, Cx, Cy, Dx, Dy;
   double m, l;
   double a, b, c, d;
   double S, T, U1, U2, V1, V2;
   double h, k, val1, val2, val3, val4;

   printf("Ax = "); scanf("%lf", &Ax);
   printf("Ay = "); scanf("%lf", &Ay);
   printf("Cx = "); scanf("%lf", &Cx);
   printf("Cy = "); scanf("%lf", &Cy);

   if ((Ax == Cx) && (Ay == Cy)) {
      printf("A and C must be two different points\n");
      exit(1);
   }

   if (Ay == Cy) {
      Bx = Dx = (Ax + Cx) / 2;
      By = Ay + (Cx - Ax) / 2;
      Dy = Ay - (Cx - Ax) / 2;
   } else {
      m = (Ax - Cx) / (Cy - Ay);
      l = (Ay + Cy) / 2 - m * (Ax + Cx) / 2;
      a = 1 + m*m;
      b = -(Ax+Cx) + m*(2*l-(Ay+Cy));
      c = (Ax+Cx)*(Ax+Cx)+(2*l-(Ay+Cy))*(2*l-(Ay+Cy));
      c -= (Ax-Cx)*(Ax-Cx)+(Ay-Cy)*(Ay-Cy);
      c /= 4;
      d = sqrt(b*b - 4*a*c);
      Bx = (-b + d) / (2 * a); By = m * Bx + l;
      Dx = (-b - d) / (2 * a); Dy = m * Dx + l;
   }

   printf("The four corners of the square are:\n");
   printf("\tA = (%lf,%lf)\n", Ax, Ay);
   printf("\tB = (%lf,%lf)\n", Bx, By);
   printf("\tC = (%lf,%lf)\n", Cx, Cy);
   printf("\tD = (%lf,%lf)\n", Dx, Dy);

   if (Ax == Bx) { S = 1; T = 0; }
   else if (Ay == By) { S = 0; T = 1; }
   else { S = (Ay - By) / (Bx - Ax); T = 1; }
   U1 = -(S * Ax + T * Ay); U2 = -(S * Dx + T * Dy);
   V1 = S * Ay - T * Ax; V2 = S * By - T * Bx;

   printf("The four sides of the square are:\n");
   printf("\tAB: "); prettyprint(S, T, U1);
   printf("\tBC: "); prettyprint(T, -S, V2);
   printf("\tCD: "); prettyprint(S, T, U2);
   printf("\tDA: "); prettyprint(T, -S, V1);

   printf("Enter the coordinates of P:\n");
   printf("\th = "); scanf("%lf", &h);
   printf("\tk = "); scanf("%lf", &k);
   val1 = S * h + T * k + U1; val2 = S * h + T * k + U2;
   val3 = T * h - S * k + V1; val4 = T * h - S * k + V2;
   if ((val1 * val2 > 0) || (val3 * val4 > 0))
      printf("+++ P lies outside the square\n");
   else if ((val1 * val2 < 0) && (val3 * val4 < 0))
      printf("+++ P lies inside the square\n");
   else
      printf("+++ P lies on the boundary of the square\n");

   exit(0);
}