import java.*;
import java.awt.*;


public class Proof2 extends java.applet.Applet  {
   Thread nineptdemo;
   Button continuebutton, restartbutton;
   Button ah2ombutton, hppkbutton; 
   int state;  
	Proof2Canvas displayer;


   public void init() {
	setBackground(Color.lightGray);
	displayer = new Proof2Canvas();
	state = 1;
	add(displayer);	  	
      continuebutton=new Button("Continue");
      restartbutton=new Button("Restart");
 
     add(continuebutton);
     add(restartbutton); 
       ah2ombutton = new Button("AH=2OM");
       add(ah2ombutton);  
       hppkbutton = new Button("HP=PK");
       add(hppkbutton);

     repaint();
   }
// state index:
// state 1 - present drawing of triangle
// state 2 - LNEF is a rectangle 
// state 3 - L,M,N,D,E,F all on circle
// state 4 - P,Q,R on circle
// state 5 - All done, show the circle
// state 21 - explain AH = 2 OL
// state 41 - explain HP=PK



   public void addstate2buttons(){
       ah2ombutton.show();

   }

   public void removestate2buttons(){
       ah2ombutton.hide();
   } 

   public void addstate4buttons(){
       hppkbutton.show();

   }

   public void removestate4buttons(){
       hppkbutton.hide();
   }

   public boolean action(Event ev, Object arg){
       if(ev.target instanceof Button  && state > 0){
          if("Continue".equals(arg)){
             switch(state){
                case 1:   addstate2buttons();
                
                
                          state++;
                          break;
               case 2:    removestate2buttons();
                          state = 3;
                          break;
                             
               case 21:   addstate2buttons();
                          state = 2;
                          break;
               case 3:
               case 41:   addstate4buttons();
                          state = 4;
                          break;
               case 4:    removestate4buttons();
                          state = 5;
                          break;
               case 5:    continuebutton.hide();
                          state = 6;
                          break;
               default:
             }
                        
          }
          if("Restart".equals(arg)){
             if(state == 2){
                removestate2buttons();
             }
             if(state == 4){
                removestate4buttons();
             }
             if(state == 6){
                continuebutton.show();
             }
             state = 1;
          }
          if("AH=2OM".equals(arg)){
             removestate2buttons();          
             state = 21;
          }
          if("HP=PK".equals(arg)){
             removestate4buttons();
             state = 41;
          }
	displayer.setState(state);
          repaint();
          return true;
       }
       return false;
   }

	public void paint(Graphics g){
		if(state == 1){
       ah2ombutton.hide();
        hppkbutton.hide();
		}

		displayer.repaint();
	}

}

class Proof2Canvas extends Canvas{
	   int state;  
   Font font;  
   int fsize;

   DPoint a,b,c;
   DPoint l,m,n;
   DPoint p,q,r;
   DPoint h;
   DPoint d,e,f;
   DLine sideab,sidebc,sideca,altap,altbq,altcr;
   DLine eh, ol, lm, mn, nl,om, on, ah,dh,oh,dm;
   DLine hp, ak, bk, ok, xp, hk;
   DPoint center,o,k;
   double radius, s;

	public Proof2Canvas(){
      resize(550,300);
      font = new Font("TimesRoman", Font.PLAIN, 12);
      fsize = 2+font.getSize();

    state = 1;      
      a = new DPoint(40.0,20.0,"A");
      b = new DPoint(270.0,20.0,"B");
      c = new DPoint(120.0,150.0,"C");
      sideab = new DLine(a,b);
     sidebc = new DLine(b,c);
      sideca = new DLine(c,a);
      l = sideab.midpoint();
      m = sidebc.midpoint();
      n = sideca.midpoint();
      l.label = "L";
      m.label = "M";
      n.label = "N";
      r = sideab.footalt(c);
      p = sidebc.footalt(a);
      q = sideca.footalt(b);
      p.label = "P";
      q.label = "Q";
      r.label = "R";
      altap = new DLine(a,p);
      altbq = new DLine(b,q);
      altcr = new DLine(c,r);
      h = altap.intersect(altbq);
      h.label = "H";
      d = new DLine(a,h).midpoint();
      e = new DLine(b,h).midpoint();
      f = new DLine(c,h).midpoint();
      d.label = "D";
      e.label = "E";
      f.label = "F";
      center = l.circumcenter(m,n);
      center.label = "X";
      o = a.circumcenter(b,c);
      o.label = "O";
      radius = center.dist(l);
      s = o.dist(a);
      eh = new DLine(e,h);
      om = new DLine(o,m);
      lm = new DLine(l,m);
      mn = new DLine(m,n);
      nl = new DLine(n,l);
      ol = new DLine(o,l);
      on = new DLine(o,n);
      ah = new DLine(a,h);
      dh = new DLine(d,h);
      oh = new DLine(o,h);
      dm = new DLine(d,m);
      hp = new DLine(h,p);
      
      // Read the proof to see why this next thing works.
      k = hp.lambdapoint(2.0);  
      k.label = "K";
      ak = new DLine(a,k);
      bk = new DLine(b,k);
      ok = new DLine(o,k);
      xp = new DLine(center,p);
      hk = new DLine(h,k);

	}

	public void setState(int s){
		state = s;
	}

   public void draw1(Graphics g) {
      g.setColor(Color.black);
      g.setFont(font);
      sideab.Show(g);
      sidebc.Show(g);
      sideca.Show(g);
      a.Show(g,7);
      b.Show(g,1);
      c.Show(g,4);
      g.setColor(Color.red);
      g.drawString("L,M,N are the midpoints of the sides.",300,20);            
      l.Show(g,0);
      m.Show(g,3);
      n.Show(g,5);
      g.setColor(Color.green);
      g.drawString("P,Q,R are the feet of the altitudes.",300, 20+fsize);
      p.Show(g,3);
      q.Show(g,5);
      r.Show(g,0);
      altap.Show(g);
      altbq.Show(g);
      altcr.Show(g);
      g.setColor(Color.blue);
      h.Show(g,7);
      g.drawString("H is the orthocenter.",300,20+2*fsize);
      g.setColor(Color.cyan);
      d.Show(g,1);
      e.Show(g,7);
      f.Show(g,3);
      g.drawString("D,E,F are the midpoints of AH, BH and CH.",300,20+3*fsize);
      g.setColor(Color.magenta);
      o.Show(g,0); 
      g.drawOval( (int)(o.x-s),(int)(o.y-s),(int)(2.0*s),(int)(2.0*s));      
      g.drawString("O is the circumcenter. The circumcircle is shown.",300,20+4*fsize);
  }

   public void draw2(Graphics g){

      
      draw1(g);
      g.setColor(Color.black);
      g.drawString("We have AH=2OM. Since D bisects AH, we have DH=OM.",10,180);
      g.setColor(Color.red);      
      ah.Show(g);
      om.Show(g);      
   }

   public void draw3(Graphics g){
      draw1(g);
      g.setColor(Color.red);
      om.Show(g);
      dh.Show(g);
      oh.Show(g);
      dm.Show(g);
      center.Show(g,4);
      g.setColor(Color.black);
      g.drawString("So DH=OM. Also DH || OM because both are perpendicular to BC.",10,180);
      g.drawString("Therefore the diagonals OH, DM bisect each other at a point X.",10,180+fsize);

   }
   public void draw4(Graphics g){
      draw1(g);
      g.setColor(Color.red);
      oh.Show(g);
      dm.Show(g);
      ak.Show(g);
      k.Show(g,4);
      center.Show(g,4);
      g.setColor(Color.black);
      g.drawString("OH, DM bisect each other at a point X, so XD=XM. Also XP=XD=XM because",10,180);
      g.drawString("angle DPM is a right angle (AP is an altitude).",10,180+fsize);
      g.drawString("Extend AP to meet the circumcircle at point K. Then we have HP=PK.",10,180+2*fsize);    
   }

   public void draw5(Graphics g){
      draw1(g);
      g.setColor(Color.red);
      center.Show(g,3);
      k.Show(g,3);
      ok.Show(g);
      hk.Show(g);
      xp.Show(g);
      oh.Show(g);
      g.setColor(Color.black);
      g.drawString("X is the midpoint of HO, and P is the midpoint of HK.",10,180);
      g.drawString("Therefore, by similar triangles HXP and HOK, XP=OK/2=",10,180+fsize);
      g.drawString("circumradius/2.",10,180+2*fsize);
      g.drawString("Now if we do the same thing with Q,N and E that we just",10,180+3*fsize);
      g.drawString("did with P,M and D, we get the same center X and the same",10,180+4*fsize);
      g.drawString("radius circumradius/2. And similarly with R,L and F.",10,180+5*fsize); 
   }

   public void draw6(Graphics g){
      draw1(g);
      g.setColor(Color.magenta);
      g.drawOval( (int)(center.x-radius),(int)(center.y-radius),(int)(2.0*radius),(int)(2.0*radius));      
      center.Show(g,1);
   }

   public void draw21(Graphics g){
      draw1(g);
      g.setColor(Color.red);
      ol.Show(g);
      om.Show(g);
      on.Show(g);
      lm.Show(g);
      mn.Show(g);
      nl.Show(g);
      g.setColor(Color.black);
      g.drawString("The circumcenter is the intersection of",10,180);
      g.drawString("the perpendicular bisectors of the sides",10,180+fsize);      
      g.drawString("of triangle ABC. That is, it is the intersection",10,180+2*fsize);
      g.drawString("of the altitudes of triangle LMN - so O is the",10,180+3*fsize);
      g.drawString("orthocenter of LMN. By similar triangles, AH/OM=AB/MN=2.",10,180+4*fsize);
   }
 
   public void draw41(Graphics g){
     draw1(g);
      g.setColor(Color.red);
      sideca.Show(g);
      altbq.Show(g);
      sidebc.Show(g);
      ak.Show(g);
      k.Show(g,4);
      bk.Show(g);
      g.setColor(Color.black);
      g.drawString("Angle CAP = angle CBQ because each is complementary to angle C.",10,180);
      g.drawString("Angle CAK = angle CBK because both cut off arc CK.",10,180+fsize);
      g.drawString("Therefore angle CBK = angle CBH.", 10, 180+2*fsize);
      g.drawString("Therefore triangles CBK and CBH are congruent, so HP=PK.",10,180+3*fsize);
   }

            
   public void paint(Graphics g) {
      switch (state) {
         case 1: {
            draw1(g); 
            break;          
         }
         case 2: {
            draw2(g);
            break;
         }
         case 3: {
            draw3(g);
            break;
         }
         case 4: {
            draw4(g);
            break;
         }
         case 5: {
            draw5(g);
            break;
         }
         case 6: {
            draw6(g);
            break;
         }
         case 21: {
            draw21(g);
            break;
         }
         case 41: {
            draw41(g);
            break;
         }
         default: {
            draw1(g);
            
            break;
         }
 
       }      

             
   }



}

class DPoint{
   
   double x, y;
   String label;
   public DPoint(double first, double second, String name){
      x = first;
      y = second;
      label = name;
   }
   public DPoint(double first, double second){
      x = first;
      y = second;
      label = "";
   }
   public void Show(Graphics g, int where){
      int first = (int) x;
      int second = (int) y;
      // where tells us where to place the character
      // relative to the point --- 0 = north, 1 = northeast,
      // 2 = east, ..., 7 = northwest.
       
      int xoffs[] = {0,3,5,6,-3,-10,-12,-10};
      int yoffs[] = {-5,-3,0,10,13,10,0,-3};
      int offsetx = xoffs[where];
      int offsety = yoffs[where];    
      g.drawOval(first-1,second-1,2,2);
      g.drawString(label,first+offsetx,second+offsety);
   }

   public double dist(DPoint q){
      return Math.sqrt((q.x - x)*(q.x - x) + (q.y - y)*(q.y - y));
   }

   public DPoint orthocenter(DPoint m, DPoint n){
   // orthocenter of triangle
      DLine sidemn = new DLine(m,n);
      DLine sidelm = new DLine(this,m);
      DPoint foot1 = sidemn.footalt(this);
      DPoint foot2 = sidelm.footalt(n);
      DLine alt1 = new DLine(this, foot1);
      DLine alt2 = new DLine(n, foot2);
      return alt1.intersect(alt2);
   }
      
   public DPoint circumcenter(DPoint b, DPoint c){
   // circumcenter of triangle formed by the 3 points
      DPoint l = new DLine(this,b).midpoint();
      DPoint m = new DLine(this,c).midpoint();
      DPoint n = new DLine(b,c).midpoint();
      return l.orthocenter(m,n);
   }      

}

class DLine{
   DPoint p,q;
   public DLine(DPoint first, DPoint second){
      p = first;
      q = second;
   }
   public void Show(Graphics g){
      int x1 = (int) p.x;
      int y1 = (int) p.y;
      int x2 = (int) q.x;
      int y2 = (int) q.y;
      g.drawLine(x1,y1,x2,y2);
   }
   public DPoint lambdapoint(double lambda){
      // The result is the point a fraction lambda 
      // of the way from point p to point q. For example,
      // if lambda == 0.5, we get the midpoint. In
      // vector notation, r = p*(1-lambda) + q*lambda.
      return(new DPoint(q.x*lambda + p.x*(1.0-lambda),
                    q.y*lambda + p.y*(1.0-lambda)));
   }
   public DPoint midpoint(){
      return lambdapoint(0.5);
   }
   public DPoint intersect(DLine m){
      double numerator = (m.q.x-q.x)*(m.q.y-m.p.y) - (m.q.x-m.p.x)*(m.q.y-q.y);
      double denominator = (p.x-q.x)*(m.q.y-m.p.y) - (m.q.x-m.p.x)*(p.y-q.y);
      double lambda = 1.0 - numerator / denominator;
      return( lambdapoint(lambda));
   }

   public DPoint footalt(DPoint c){
      // foot of the altitude from point c to this line
      // determine lambda so that 
      // lambdapoint h on line qp satisfies
      // dot product ch.pq == 0.
      double lambda = ( (q.x-p.x)*(q.x-c.x)
          + (q.y-p.y)*(q.y-c.y) )
          /
          ( (q.x-p.x)*(q.x-p.x) + (q.y-p.y)*(q.y-p.y) );
      return lambdapoint(1.0-lambda);
   }
}