unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls, Math, ExtCtrls, Mask, JvExMask, JvSpin;

type
  TModPoint = record
    X: Real;
    Y: Real;
  end;
  TForm1 = class(TForm)
    Button1: TButton;
    Panel1: TPanel;
    Label1: TLabel;
    JvSpinEdit1: TJvSpinEdit;
    Label2: TLabel;
    Image1: TImage;
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

function PointToModPoint(Point: TPoint): TModPoint;
var
  X, Y: Real;
  ResPoint: TModPoint;
begin
  X := (Point.X-200)/200;
  Y := (200-Point.Y)/200;

  ResPoint.X := X;
  ResPoint.Y := Y;

  Result := ResPoint;
end;

function CheckPoint(ModPoint: TModPoint): Boolean;
begin
  if ((ModPoint.Y >= 0) and (ModPoint.X >= 0)) or ((ModPoint.Y >= 0) and (ModPoint.X <= 0)) then
  begin
    if ModPoint.Y <= Sin(ArcCos(ModPoint.X)) then
    Result := True else Result := False;
  end else
  if ((ModPoint.Y <= 0) and (ModPoint.X <= 0)) or ((ModPoint.Y <= 0) and (ModPoint.X >= 0)) then
  begin
    if ModPoint.Y >= -Sin(ArcCos(ModPoint.X)) then
    Result := True else Result := False;
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  Point: TPoint;
  I, Counter, Max: Integer;
begin
  Randomize;
  Image1.Canvas.Fillrect(Image1.Canvas.ClipRect);
  Image1.Canvas.Ellipse(0,0,400,400);
  Counter := 0;
  Max := StrToInt(FloatToStr(JvSpinEdit1.Value));
  for I := 1 to Max do
  begin
    Point.X := Random(400);
    Point.Y := Random(400);
    if CheckPoint(PointToModPoint(Point)) = True then
    begin
      Counter := Counter+1;
      Image1.Canvas.Pixels[Point.X, Point.Y] := clRed;
    end
    else
      Image1.Canvas.Pixels[Point.X, Point.Y] := clBlue;
    Label2.Caption := Format('Tirs: %d || Encerts: %d', [I, Counter]);
    Label2.Repaint;
    Image1.Repaint;
  end;
  ShowMessage(FloatToStr((Counter/Max)*4));
end;

end.