Построение прямой, которая касается двух заданных окружностей

#include <vcl.h>
#pragma hdrstop 
#include "Unit1.h"
#include "math.h"
#include "Unit2.h"
#include "stdio.h"
  
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
float xd,yd,x1,x2,y1,y2,a,b,xt1,yt1,xt2,yt2,xt3,yt3,xt4,yt4,xmax,xmin,ymax,ymin,m=1,s;
AnsiString ozn;
 
int px(float x)
{
return x+Form2->Image1->Width/2;
}
 
int py(float y)
{
return Form2->Image1->Height/2-y;
}
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner)
        : TForm(Owner)
{ 
}
//---------------------------------------------------------------------------
 
void __fastcall TForm1::Button1Click(TObject *Sender)
{
 
float a1=10, a2=2,a3, a4, b1=100, b2=50, xp, yp, l1, l2, l3, r=100, rr=100, x0, y0,xd,yd;
a1=StrToFloat(Edit1->Text)*m;
b1=StrToFloat(Edit2->Text)*m;
a2=StrToFloat(Edit3->Text)*m;
b2=StrToFloat(Edit4->Text)*m;
r=StrToFloat(Edit5->Text)*m;
rr=-(StrToFloat(Edit6->Text))*m;
  
a4= ((atan(a2)*180/M_PI+atan(a1)*180/M_PI)/2)*M_PI/180;
xp=(b2-b1)/(a1-a2);
yp=a1*xp+b1;
a3= (a4*180/M_PI-atan(a1)*180/M_PI)*M_PI/180;
l1=r/sin(a3);
l2=l1*sin(a4);
l3=l1*cos(a4);
x0=xp+l3;
y0=yp+l2;
 
//Побудова кола R
Form1->Image1->Canvas->MoveTo(xp+250,yp+250);
Form1->Image1->Canvas->Ellipse(x0-r+250,y0-r+250,x0+r+250,y0+r+250);
 
l1=rr/sin(a3);
l2=l1*sin(a4);
l3=l1*cos(a4);
x0=xp+l3;
y0=yp+l2;
 
//Побудова кола -R
Form1->Image1->Canvas->MoveTo(xp+250,yp+250);
Form1->Image1->Canvas->Ellipse(x0-rr+250,y0-rr+250,x0+rr+250,y0+rr+250);
 
 
Form1->Image1->Canvas->MoveTo(xp+250,yp+250);
for (int j=-250; j<250; j++)
{   Form1->Image1->Canvas->LineTo(j+250,a2*j+b2+250);
}
 
//
Form1->Image1->Canvas->Pen->Color=(TColor)RGB(0,0,0);
Form1->Image1->Canvas->MoveTo(0,Form1->Image1->Height/2);
Form1->Image1->Canvas->LineTo(Form1->Image1->Width,Form1->Image1->Height/2);
Form1->Image1->Canvas->MoveTo(Form1->Image1->Width/2,0);
Form1->Image1->Canvas->LineTo(Form1->Image1->Width/2,Form1->Image1->Height);
 
 
for (xd=0; xd<=Form1->Image1->Width*m; xd=xd+50)
{
Form1->Image1->Canvas->MoveTo(px(xd*m),py(-5));
 Form1->Image1->Canvas->LineTo(px(xd*m),py(5));
 Form1->Image1->Canvas->TextOutA(px(xd*m-10),py(-10),FloatToStr(xd));
 }
for (xd=0; xd>=-Form1->Image1->Width*m; xd=xd-50)
{
Form1->Image1->Canvas->MoveTo(px(xd*m),py(-5));
 Form1->Image1->Canvas->LineTo(px(xd*m),py(5));
 Form1->Image1->Canvas->TextOutA(px(xd*m-10),py(-10),FloatToStr(xd));
 }
 
 for (yd=50; yd<=Form1->Image1->Height*m; yd=yd+50)
{
 Form1->Image1->Canvas->MoveTo(px(-5),py(yd*m));
 Form1->Image1->Canvas->LineTo(px(5),py(yd*m));
Form1->Image1->Canvas->TextOutA(px(10),py(yd*m+5),FloatToStr(yd));
 }
for (yd=-50; yd>=-Form1->Image1->Height*m; yd=yd-50)
{
Form1->Image1->Canvas->MoveTo(px(-5),py(yd*m));
 Form1->Image1->Canvas->LineTo(px(5),py(yd*m));
 Form1->Image1->Canvas->TextOutA(px(10),py(yd*m+5),FloatToStr(yd));
 }
 
}
 
 
//---------------------------------------------------------------------------
void __fastcall TForm1::Button2Click(TObject *Sender)
{
Form1->Image1->Canvas->Rectangle(0,0,800,800);
 
}
//---------------------------------------------------------------------------
 void __fastcall TForm1::N1Click(TObject *Sender)
{
Form1->Hide();
Form2->Show();
}
//---------------------------------------------------------------------------
  void __fastcall TForm1::Image1MouseMove(TObject *Sender, TShiftState Shift,
      int X, int Y)
{
int x_z = X;
int y_z= Y;
Form1->Label9->Caption="X= "+IntToStr(x_z);
Form1->Label10->Caption="Y= "+IntToStr(y_z);
}
//---------------------------------------------------------------------------
 
void __fastcall TForm1::Button3Click(TObject *Sender)
{
m=m-0.1;
 
Form1->Image1->Canvas->Rectangle(0,0,Form1->ClientWidth,Form1->Height);
Form1->Image1->Canvas->MoveTo(0,Form1->Image1->Height/2);
Form1->Image1->Canvas->LineTo(Form1->Image1->Width,Form1->Image1->Height/2);
Form1->Image1->Canvas->MoveTo(Form1->Image1->Width/2,0);
Form1->Image1->Canvas->LineTo(Form1->Image1->Width/2,Form1->Image1->Height);
 
 
 Button1Click(0);
 
}
//---------------------------------------------------------------------------
 
void __fastcall TForm1::Button4Click(TObject *Sender)
{
 
m=m+0.1;
 
Form1->Image1->Canvas->Rectangle(0,0,Form1->Width,Form1->Height);
Form1->Image1->Canvas->MoveTo(0,Form1->Image1->Height/2);
Form1->Image1->Canvas->LineTo(Form1->Image1->Width,Form1->Image1->Height/2);
Form1->Image1->Canvas->MoveTo(Form1->Image1->Width/2,0);
Form1->Image1->Canvas->LineTo(Form1->Image1->Width/2,Form1->Image1->Height);
 
 Button1Click(0);
 
}
//---------------------------------------------------------------------------

Form1->Image1->Canvas->MoveTo(xp+250,yp+250);
Form1->Image1->Canvas->Ellipse(x0-r+250,y0-r+250,x0+r+250,y0+r+250);

Ellipse(x0-r+250,y0-r+250,x0+r+250,y0+r+250)

//Побудова кола R
Form1->Image1->Canvas->MoveTo(xp+250,yp+250);
Form1->Image1->Canvas->Ellipse(x0-r+250,y0-r+250,x0+r+250,y0+r+250);
// ставим точку!!!
Form1->Image1->Canvas->Pixels[x0+250][y0+250]=clRed;

//Побудова кола -R
Form1->Image1->Canvas->MoveTo(xp+250,yp+250);
Form1->Image1->Canvas->Ellipse(x0-rr+250,y0-rr+250,x0+rr+250,y0+rr+250);
// ставим точку!!!
Form1->Image1->Canvas->Pixels[x0+250][y0+250]=clRed;