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


public class Proof1 extends java.applet.Applet  {
	Proof1Canvas displayer;
	int state;
	Button LNEFbutton;
	Button LENFbutton;
	Button LELNbutton;
	Button continuebutton;
	Button restartbutton;

	public void init(){
		state = 1;
		displayer = new Proof1Canvas();
		displayer.resize(550,300);
		add(displayer);
		continuebutton=new Button("Continue");
		restartbutton=new Button("Restart");
 
		add(continuebutton);
		add(restartbutton);  

		LNEFbutton = new Button("LN || EF");
		LENFbutton = new Button("LE || NF");
		LELNbutton = new Button("LE per. LN");
		add(LNEFbutton);
		add(LENFbutton);
		add(LELNbutton);

		setBackground(Color.lightGray);


	}

	public void addstate2buttons(){
       LNEFbutton.show();
       LENFbutton.show();
       LELNbutton.show();
   }

   public void removestate2buttons(){
          LNEFbutton.hide();
       LENFbutton.hide(); 
       LELNbutton.hide();

   } 


	public void paint(Graphics g){
		if(state==1)
			removestate2buttons();
		displayer.repaint();
	}

	   public boolean action(Event ev, Object arg){
       if(ev.target instanceof Button  && state > 0){
          if("Continue".equals(arg)){
             switch(state){
                case 1:   addstate2buttons();
                case 3:
                case 21:
                case 23:  state++;
                          break;
               case 2:    removestate2buttons();
                          state = 3;
                          break;
                             
               case 25: 
               case 22:           
               case 24:   addstate2buttons();
                          state = 2;
                          break;
               case 4:    
                          state = 5;
						  continuebutton.hide();
                          break;
               default:
             }
		  }
		  if("Restart".equals(arg)){
             if(state == 2){
                removestate2buttons();
             }
             if(state == 5){
				continuebutton.show();
             }
             state = 1;
          }
		if("LN || EF".equals(arg)){
             removestate2buttons();          
             state = 21;
          }
          if("LE || NF".equals(arg)){
             removestate2buttons();          
             state = 23;
          }
          if("LE per. LN".equals(arg)){
             removestate2buttons();          
             state = 25;
          }
 
                        
          
		  displayer.setState(state);
		  repaint();
          return true;
       }
       return false;
   }



}




class Proof1Canvas 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 ln,ef,le,nf,bh,ch, ah,lm,mf,fd,dl,dm,dp,pm;
   DPoint center;
   double radius;
 
public Proof1Canvas(){
	      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 = "CENTER";
      radius = center.dist(l);
      ln = new DLine(l,n);
      ef = new DLine(e,f); 
      le = new DLine(l,e);
      nf = new DLine(n,f);
      bh = new DLine(b,h);
      ch = new DLine(c,h);
      ah = new DLine(a,h);
      lm = new DLine(l,m);
      mf = new DLine(m,f);
      fd = new DLine(f,d);
      dl = new DLine(d,l);
      dm = new DLine(d,m);
      dp = new DLine(d,p);
      pm = new DLine(p,m);
}

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 21: {
            draw21(g);
            break;
         }
         case 22: {
            draw22(g);
            break;
         }
         case 23: {
            draw23(g);
            break;
         }
         case 24: {
            draw24(g);
            break;
         }
         case 25: {
            draw25(g);
            break;
         }



	  }
  }
	  

	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);
   }


   public void draw2(Graphics g){

      
      draw1(g);
      g.setColor(Color.black);
      g.drawString("For more explanation, press a button.",10,180);
      g.drawString("We have LN || EF, LE || NF and LE perpendicular to LN.",10,180+fsize);
      g.drawString("Therefore LNFE is a rectangle.",10,180+2*fsize);
      g.setColor(Color.orange);      
      ln.Show(g);
      ef.Show(g);
      le.Show(g);
      nf.Show(g);      
   }

   public void draw3(Graphics g){
      draw1(g);
      g.setColor(Color.orange);      
      ln.Show(g);
      ef.Show(g);
      le.Show(g);
      nf.Show(g);      
     g.setColor(Color.black);
      g.drawString("We have that LNFE is a rectangle; similarly, LMFD is a rectangle.",10,180+fsize);
      g.drawString("Therefore L,M,N,D,E, and F are all on the circle with diameter LF",10,180+2*fsize);
      g.drawString("because LF is a diagonal of both rectangles, so that all 6 points",10,180+3*fsize);
      g.drawString("at the vertices of the rectangles are equidistant from the midpoint of LF.",10,180+4*fsize);
      g.setColor(Color.red);
      lm.Show(g);
      mf.Show(g);
      fd.Show(g);
      dl.Show(g);
   }
   public void draw4(Graphics g){
      draw1(g);
      g.setColor(Color.black);
      g.drawString("Finally, P, Q and R are on the circle with diameter LF.",10,180);
      g.drawString("For point P, since AP is an altitude of triangle ABC,",10,180+fsize);
      g.drawString("angle DPM is a right angle. Since the diameter DM of the",10,180+2*fsize);
      g.drawString("subtends a right angle at P, P must be on the circle.",10,180+3*fsize);       
      g.drawString("Similarly, Q and R are on the circle.",10,180+4*fsize);
      g.setColor(Color.red); 
      dm.Show(g);
      dp.Show(g);
      pm.Show(g);
   }

   public void draw5(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.orange);
      ln.Show(g);
      sidebc.Show(g);
      sideab.Show(g);
      sideca.Show(g);
      g.setColor(Color.black);
      g.drawString("LN || BC because LN joins the midpoints",10,180);
      g.drawString("of two sides AB, AC of triangle ABC.",10,180+fsize);      
   }
   public void draw22(Graphics g){
      draw1(g);
      g.setColor(Color.orange);
      sidebc.Show(g);
      bh.Show(g);
      ch.Show(g);
      ef.Show(g);
      g.setColor(Color.black);
      g.drawString("LN || BC because LN joins the midpoints",10,180);
      g.drawString("of two sides AB, AC of triangle ABC.",10,180+fsize);      
      g.drawString("EF || BC because E,F are the midpoints",10,180+2*fsize);
      g.drawString("of two sides BH, CH of triangle BCH.",10,180+3*fsize);
      g.drawString("Therefore LN || EF because both are || BC.",10,180+4*fsize);
   }
   public void draw23(Graphics g){
      draw1(g);
      g.setColor(Color.orange);
      le.Show(g);
      ah.Show(g);
      sideab.Show(g);
      bh.Show(g);
      g.setColor(Color.black);
      g.drawString("LE || AH because LE joins the midpoints",10,180);
      g.drawString("of two sides AB, BH of triangle ABH.",10,180+fsize);      
   }
   public void draw24(Graphics g){
      draw1(g);
      g.setColor(Color.orange);
      sideca.Show(g);
      ah.Show(g);
      ch.Show(g);
      nf.Show(g);
      g.setColor(Color.black);
      g.drawString("LE || AH because LE joins the midpoints",10,180);
      g.drawString("of two sides AB, BH of triangle ABH.",10,180+fsize);      
      g.drawString("NF || AH because N,F are the midpoints",10,180+2*fsize);
      g.drawString("of two sides AC, CH of triangle ACH.",10,180+3*fsize);
      g.drawString("Therefore LE || NF because both are || BC.",10,180+4*fsize);
   }

   public void draw25(Graphics g){
      draw1(g);
      g.setColor(Color.orange);
      le.Show(g);
      ln.Show(g);
      sidebc.Show(g);
      g.setColor(Color.black);
      g.drawString("We have LE || AP (see the proof that LE || NF),",10,180);
      g.drawString("AP perpendicular to BC (AP is an altitude),",10,180+fsize);
      g.drawString("and BC || LN (from the proof that LN || EF).",10,180+2*fsize);
      g.drawString("Therefore LE is perdendicular to LN.",10, 180+4*fsize);
   }
      
 
}


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);
   }
}