Chords, first method (1 point + 1 point)

unit ChordUnit;

interface

uses
  Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants, System.Classes, Vcl.Graphics,
  Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.ExtCtrls, Vcl.StdCtrls;

type
  TMainForm = class(TForm)
    ChordImage: TImage;
    RunButton: TButton;
    AnswerLabel: TLabel;
    NumberLabel: TLabel;
    procedure RunButtonClick(Sender: TObject);
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  MainForm: TMainForm;

implementation
const
    RADIUS = 330;
    MAX_RANGE = High(Integer);
var
    XCenter, YCenter: Word;
    ChordCount, LongChordCount: Integer;
    Side: Real;
{$R *.dfm}

procedure GetRandomCoordOutsideCircle(var XPoint: Integer; var YPoint: Integer);
var
    Coef: Integer;
begin
    repeat
        XPoint := Random(MAX_RANGE);
        YPoint := Random(MAX_RANGE);
    until Sqr(XPoint) + Sqr(YPoint) > Sqr(RADIUS);

    Coef := Random(2);
    if Coef = 1 then
        XPoint := XCenter - Abs(XPoint)
    else
        XPoint := XCenter + Abs(XPoint);

    Coef := Random(2);
    if Coef = 1 then
        YPoint := YCenter - Abs(YPoint)
    else
        YPoint := YCenter + Abs(YPoint);
end;

procedure GetRandomCoordOnCircumference (var XPoint: Integer; var YPoint: Integer);
var
    Coef: Integer;
begin
    Coef := Random(2);
    if Coef = 1 then
    begin
        XPoint := Random(RADIUS);
        YPoint := Trunc(Sqrt(Sqr(RADIUS) - Sqr(XPoint)));
    end
    else
    begin
        YPoint := Random(RADIUS);
        XPoint := Trunc(Sqrt(Sqr(RADIUS) - Sqr(YPoint)))
    end;

    Coef := Random(2);
    if Coef = 1 then
        XPoint := XCenter - Abs(XPoint)
    else
        XPoint := XCenter + Abs(XPoint);

    Coef := Random(2);
    if Coef = 1 then
        YPoint := YCenter - Abs(YPoint)
    else
        YPoint := YCenter + Abs(YPoint);
end;

procedure ConnectChord(X0, Y0, X1, Y1: Integer);
var
    XL, XR, X, Y, Coef: Integer;
    K, C, A, ChordLength: Real;
begin
    X0 := X0 - XCenter;
    Y0 := Y0 - YCenter;
    X1 := X1 - XCenter;
    Y1 := Y1 - YCenter;

    if X1-X0 <> 0 then
    begin
        K := (Y1-Y0)/(X1-X0);
        C := Y0 - K*X0;
        A := 1 + K*K;

        XL := Trunc((-K*C - Sqrt(K*K*RADIUS*RADIUS - C*C + RADIUS*RADIUS)) / A);
        XR := Trunc((-K*C + Sqrt(K*K*RADIUS*RADIUS - C*C + RADIUS*RADIUS)) / A);

        if X1 > 0 then
            X := XL
        else
            X := XR;

        Y := Trunc(Sqrt(RADIUS*RADIUS - X*X));
        Coef := Random(2);
        if Coef = 1 then
            Y := - Abs(Y)
        else
            Y := Abs(Y);

        ChordLength := Sqrt(Sqr(X - X1) + Sqr(Y-Y1));

        X := X + XCenter;
        Y := Y + YCenter;
        X1 := X1 + XCenter;
        Y1 := Y1 + YCenter;

        with MainForm.ChordImage.Canvas do
        begin
            Pen.Color := clBlue;
            MoveTo(X, Y);
            LineTo(X1, Y1);
        end;

        if ChordLength > Side then
            Inc(LongChordCount);
        Inc(ChordCount);
    end;
end;

procedure DrawChord;
var
    XPoint, YPoint, XCyclePoint, YCyclePoint: Integer;
begin
    with MainForm.ChordImage.Canvas do
    begin
        GetRandomCoordOutsideCircle(XPoint, YPoint);
        Pen.Color := clBlack;
        Ellipse(XPoint-2, YPoint-2, XPoint+2, YPoint+2);

        GetRandomCoordOnCircumference(XCyclePoint, YCyclePoint);
        Pen.Color := clRed;
        Ellipse(XCyclePoint-2, YCyclePoint-2, XCyclePoint+2, YCyclePoint+2);


        ConnectChord(XPoint, YPoint, XCyclePoint, YCyclePoint);
    end;
end;

procedure TMainForm.FormCreate(Sender: TObject);
begin
    Randomize;
    XCenter := MainForm.ChordImage.Width Div 2;
    YCenter := MainForm.ChordImage.Height Div 2;

    ChordCount := 0;
    LongChordCount := 0;
    Side := RADIUS * Sqrt(3);
end;

procedure TMainForm.RunButtonClick(Sender: TObject);
var
    I: Integer;
begin
    with ChordImage do
    begin
        Canvas.Ellipse(XCenter - RADIUS, YCenter - RADIUS, XCenter + RADIUS, YCenter + RADIUS);
        Canvas.Pen.Color := clBlack;
    end;
        I := 0;
        repeat
            DrawChord;
            Inc(I);
        until I = 1000;

   NumberLabel.Caption := IntToStr(LongChordCount) + '/' + IntToStr(ChordCount) + '=' + FloatToStr(LongChordCount/ChordCount);
end;

end.