/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;

P proj(const P& arg)
{
  return P(2*arg.x1()/(1 - arg.x2()), -1);
}

int main()
{
  picture(P(-3, -1), P(3, 1), "4.5 x 1.5in");

  begin();
  bold();
  P pP(0,1), pQ(0,-1), pP2(2.5,1), pQ2(-2.25,-1);

  Circle C(P(0,0), 1);
  Segment L1(pP2, pQ2), L2(L1*C);
  P pM(L2.end2()), pN(L2.end1()), pX(proj(pM)), pY(proj(pN));

  line(P(xmin(),-1), P(xmax(),-1));
  line(P(xmin(), 1), P(xmax(), 1));

  C.draw();
  L1.draw();
  line(pP, pQ);
  line(pN, pQ);

  line(pP, pX);
  line(pP, pY);

  label(pQ2, P(0,-4), "$Q'$", b);
  label(pQ, P(0,-4), "$Q$", b);
  label(pX, P(0,-4), "$X$", b);
  label(pY, P(0,-4), "$Y$", b);

  label(pP, P(0, 2), "$P$", t);
  label(pP2, P(0, -2), "$P'$", br);

  label(pN, P(-2, -10), "$N$", b);
  label(pM, P(-4, -6), "$M$", b);

  tikz_format();
  end();
}