Написать программу, определяющую радиус и центр окружности, проходящей по крайней мере через три различные точки заданного множества точек

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#include <vcl.h>
#pragma hdrstop
 
#include "Unit1.h"
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner)
    : TForm(Owner)
{
}
//---------------------------------------------------------------------------
double koef(TPoint a, TPoint b)
{
  return (b.y-a.y)*1./(b.x-a.x);
}
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int centerX(double koefa, double koefb, TPoint a, TPoint b, TPoint c)  // koefa == koef21, koefb == koef32
{
  return (koefa*koefb*(a.y-c.y)+koefb*(a.x+b.x)-koefa*(b.x+c.x))/2/(koefb-koefa);
}
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int centerY(double koefa, int x, TPoint a, TPoint b)
{
  return -(x-(a.x+b.x)/2.)/koefa+(a.y+b.y)/2.;
}
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int radius(TPoint a, TPoint b)
{
  return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
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struct CR
{
  TPoint center;
  int radius, count;
}id;
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const n = 25, p = 750;
TPoint z[n];
CR InnerDots(int exclude_corner)
{
  CR cr;
  TPoint temp[3], corner[3], center;
  switch (exclude_corner)
  {
    case 0:
      corner[0] = TPoint(p, 0);
      corner[1] = TPoint(0, p);
      corner[2] = TPoint(p, p);
      break;
    case 1:
      corner[0] = TPoint(0, 0);
      corner[1] = TPoint(0, p);
      corner[2] = TPoint(p, p);
      break;
    case 2:
      corner[0] = TPoint(0, 0);
      corner[1] = TPoint(p, 0);
      corner[2] = TPoint(p, p);
      break;
    case 3:
      corner[0] = TPoint(0, 0);
      corner[1] = TPoint(p, 0);
      corner[2] = TPoint(0, p);
  }
/*  corner[0] = TPoint(0, 0);
  corner[1] = TPoint(p, 0);
  corner[2] = TPoint(0, p);
  corner[3] = TPoint(p, p);*/
  double k1, k2, angle;
  int r, i, j, count = 0;
 
  center.x = p/2;
  center.y = p/2;
  for (i = 0; i < 4; i++)
    temp[i] = center;
 
  for (i = 0; i < n; i++)
    for (j = 0; j < 3; j++)
      if (radius(z[i], corner[j]) > radius(temp[j], corner[j]))
        temp[j] = z[i];
 
  k1 = koef(temp[0], temp[1]);
  k2 = koef(temp[1], temp[2]);
  center.x = centerX(k1, k2, temp[0], temp[1], temp[2]);
  center.y = centerY(k1, center.x, temp[0], temp[1]);
  r = radius(center, temp[0]);
  cr.center = center;
  cr.radius = r;
 
  for (i = 0; i < n; i++)
    if (radius(z[i], center) <= r+1)  // r+1, а не r - чтобы сократить влияние округлений при подсчете точек
      count++;
  cr.count = count;
  return cr;
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Button1Click(TObject *Sender)
{
  ClientHeight = p;
  ClientWidth = p;
  TPoint center;
  double angle;
  int r, i, count = 0;
  InvalidateRect(NULL, NULL, 1);
 
  randomize();
  for (i = 0; i < n; i++)
  {
    z[i].x = random(p/2)+p/4;
    z[i].y = random(p/2)+p/4;
    Canvas->Pixels[z[i].x][z[i].y] = clBlack;
  }
 
  for (i = 0; i < 4; i++)
  {
    id = InnerDots(i);
    if (id.count > count)
    {
      count = id.count;
      center = id.center;
      r = id.radius;
    }
    if (id.count == n)
      break;
  }
 
  for (i = 0; i < 100000; i++)
  {
    angle = 2*M_PI*i/p;
    Canvas->Pixels[r*cos(angle)+center.x][r*sin(angle)+center.y] = clRed;
  }
 
  Caption = "Окружность: радиус R = " + String(r) + ", центр - (" + String(center.x) + ", " + String(center.y) + "), точек внутри окружности - " + String(count);
}
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