Как рассчитать все параметры треугольника?

Для расчета основных параметров треугольника (таких как: периметр, площадь, длины сторон, углы, координаты, радиусы вписанной и описанной окружностей, а также координаты их центров) можно воспользоваться следующим классом TTriangle. Все формулы, используемые в коде, а также пример работы класса в практической реализации см. на странице "Расчет треугольника"

 
TTriangle = class
  private
    fx1, fy1 : Double;
    fx2, fy2 : Double;
    fx3, fy3 : Double;
    function GetDistAB: Double;
    function GetDistAC: Double;
    function GetDistBC: Double;
    function GetPerimeter: Double;
    function GetArea: Double;
    function GetAngleA: Double;
    function GetAngleB: Double;
    function GetAngleC: Double;
    function GetRadiusIn: Double;
    function GetRadiusOut: Double;
    function GetCenterOut: TFPoint;
    function GetCenterIn: TFPoint;
    function PointsInLine: Boolean;
  public
    // Задание треугольника координатами его вершин
    constructor Create( ax1,ay1, ax2,ay2, ax3,ay3: Double); overload;
    // Задание треугольника длинами его сторон
    constructor Create( a, b, c: Double); overload;
    //функция нахождения длины отрезка
    function Dist( ax1, ay1, ax2, ay2: Double): Double;   
  published
    // координаты первой вершины A
    property X1: Double read fx1 write fx1;
    property Y1: Double read fy1 write fy1;
    // координаты второй вершины B
    property X2: Double read fx2 write fx2;
    property Y2: Double read fy2 write fy2;
    // координаты третьей вершины С
    property X3: Double read fx3 write fx3;
    property Y3: Double read fy3 write fy3;
    property DistAB: Double read GetDistAB; // Длина AB
    property DistBC: Double read GetDistBC; // Длина BC
    property DistAC: Double read GetDistAC; // Длина AC
    property Perimeter: Double read GetPerimeter; // Периметр
    property Area: Double read GetArea;  // Площадь
    property AngleA: Double read GetAngleA; // Угол A
    property AngleB: Double read GetAngleB; // Угол B
    property AngleC: Double read GetAngleC; // Угол C
    // Радиус вписанной окружности
    property RadiusIn: Double read GetRadiusIn;
    // Радиус описанной окружности 
    property RadiusOut: Double read GetRadiusOut;
    // Центр описанной окружности
    property CenterOut: TFPoint read  GetCenterOut;
    // Центр вписанной окружности
    property CenterIn: TFPoint read  GetCenterIn;
  end;
 
{ TTriangle }
 
constructor TTriangle.Create(ax1, ay1, ax2, ay2, ax3, ay3: Double);
begin
  fx1 := ax1;
  fy1 := ay1;
  fx2 := ax2;
  fy2 := ay2;
  fx3 := ax3;
  fy3 := ay3;
end;
 
 
constructor TTriangle.Create(a, b, c: Double);
Var cosa: Double;
begin
  fx1 := 0;
  fy1 := 0;
  fx2 := 0;
  fy2 := c;
  cosa := (b*b+c*c - a*a)/(2*b*c);
  fy3 := b * cosa;
  fx3 := b * sin(arccos(cosA));
end;
 
 
function TTriangle.Dist(ax1, ay1, ax2, ay2: Double): Double;
begin
 Result := sqrt((ax2-ax1)*(ax2-ax1)+(ay2-ay1)*(ay2-ay1));
end;
 
 
function TTriangle.GetAngleA: Double;
Var a, r: Double;
begin
 a := (fx2-fx1)*(fx3-fx1)+(fy2-fy1)*(fy3-fy1);
 r := a/DistAB/DistAC;
 Result := arccos(r);
end;
 
 
function TTriangle.GetAngleB: Double;
Var a, r: Double;
begin
 a := (fx1-x2)*(fx3-fx2)+(fy1-fy2)*(fy3-fy2);
 r := a/DistAB/DistBC;
 Result := arccos(r);
end;
 
 
function TTriangle.GetAngleC: Double;
Var a, r: Double;
begin
 a := (fx2-x3)*(fx1-fx3)+(fy2-fy3)*(fy1-fy3);
 r := a/DistBC/DistAC;
 Result := arccos(r);
end;
 
 
function TTriangle.GetArea: Double;
begin
 Result := sqrt((Perimeter/2*(Perimeter/2-DistAB)*
                (Perimeter/2-DistBC)*(Perimeter/2-DistAC)));
end;
 
 
function TTriangle.GetCenterIn: TFPoint;
Var
  Lc, Lb, La             : Double;
  cx, cy, bx, by, ax, ay : Double; 
  K1, K2                 : Double;
begin
  Lb := DistBC/DistAB;
  Lc := DistBC/DistAC;
 
  cx := (fx2+Lc*fx1)/(Lc+1);
  cy := (fy2+Lc*fy1)/(Lc+1);
 
  bx := (fx3+Lb*fx1)/(Lb+1);
  by := (fy3+Lb*fy1)/(Lb+1);
 
  if cx <> fx3 then K1 := (cy-fy3)/(cx-fx3) else K1 := 1e+96;
  if bx <> fx2 then K2 := (by-fy2)/(bx-fx2) else K2 := 1e+96;
 
  Result.x := (K1*fx3-K2*fx2+(fy2-fy3))/(K1-K2);
  if Result.x <> fx3 then
    Result.y := K1*(Result.x-fx3)+fy3
  else
    Result.y := K2*(Result.x-fx2)+fy2;
end;
 
 
function TTriangle.GetCenterOut: TFPoint;
Var ma, mb : Double;  //  коэффициенты наклона линий
begin
  if fx2 <> fx1 then ma := (fy2-fy1)/(fx2-fx1) else ma := 1e95;
  if fx3 <> fx2 then mb := (fy3-fy2)/(fx3-fx2) else mb := 1e95;
  Result.x := (ma*mb*(fy1-fy3) + mb*(fx1+fx2) - 
               ma*(fx2+fx3))/(2*(mb-ma));
  if ma <> 0 then
    Result.y :=  -1/ma*(Result.x - (fx1+fx2)/2) + (fy1+fy2)/2
  else
    Result.y :=  -1/mb*(Result.x - (fx2+fx3)/2) + (fy2+fy3)/2;
end;
 
 
function TTriangle.GetDistAB: Double;
begin
  Result := Dist ( fx1, fy1, fx2, fy2);
end;
 
 
function TTriangle.GetDistAC: Double;
begin
  Result := Dist ( fx1, fy1, fx3, fy3);
end;
 
 
function TTriangle.GetDistBC: Double;
begin
  Result := Dist ( fx2, fy2, fx3, fy3);
end;
 
 
function TTriangle.GetPerimeter: Double;
begin
  Result := DistAB + DistBC + DistAC;
end;
 
 
function TTriangle.GetRadiusIn: Double;
begin
  if not PointsInLine then
    Result := 2 * Area / Perimeter;
end;
 
 
function TTriangle.GetRadiusOut: Double;
begin
  if not PointsInLine then
    Result := (DistAB*DistBC*DistAC)/(4*Area);
end;
 
 
function TTriangle.PointsInLine: Boolean;
Var a : double;
begin
  Result := false;
  a := fx1*fy2+fx2*fy3+fx3*fy1-fx3*fy2-fx2*fy1-fx1*fy3;
  if abs(a - 1e-20) < 1e-19 then
    Result := true;
end;

Пример использования класса для задачи "Как найти площадь треугольника, заданного длинами сторон a=10, b=12, c=11?"

procedure TForm1.Button1Click(Sender: TObject);
Var T: TTriangle;
begin
   T := TTriangle.Create( 10, 12, 11);
   showmessage( FloatToStr( T.Area));
end;

Пример использования класса для задачи "Как найти периметр треугольника, заданного координатами вершин A(0,0), B(1,0), C(1,1)?"

procedure TForm1.Button1Click(Sender: TObject);
Var T: TTriangle;
begin
   T := TTriangle.Create( 0, 0, 1, 0, 1, 1);
   showmessage(FloatToStr( T.Perimeter));
end;

Отправил Waltertib Сб, 04/25/2020 - 21:53

cialis pills sale canada https://edpillsphrm.com best place buy viagra

Отправил unrejerm Сб, 04/25/2020 - 20:43

buy viagra hong kong canada pharmacy buy cialis canada

Отправил HenryWaf Сб, 04/25/2020 - 20:42

buy cialis generic buy generic ed pills online how to get cialis

Отправил Impebra Сб, 04/25/2020 - 19:42

buy viagra uk forum canadian pharmacy how to buy viagra in uk

Отправил Waltertib Сб, 04/25/2020 - 19:37

buy cialis soft online https://edpillsphrm.com how to order levitra

Отправил unrejerm Сб, 04/25/2020 - 18:31

buy female viagra https://edpillsphrm.com buy viagra nigeria

Отправил HenryWaf Сб, 04/25/2020 - 18:30

real cialis for sale buy ed pills online viagra sale america

Отправил Waltertib Сб, 04/25/2020 - 17:22

levitra 20 mg cheap https://edpillsphrm.com buy cialis mexico

Отправил Impebra Сб, 04/25/2020 - 16:49

cheap viagra cialis levitra generic viagra 100mg order cialis india

Отправил unrejerm Сб, 04/25/2020 - 16:35

buy viagra super force online https://edpillsphrm.com canadian pharmacy viagra

Отправил HenryWaf Сб, 04/25/2020 - 16:16

buy cialis without prescriptions https://edpillsphrm.com buy cialis fda

Отправил Waltertib Сб, 04/25/2020 - 15:05

where do i buy viagra yahoo https://edpillsphrm.com viagra buy boots

Отправил unrejerm Сб, 04/25/2020 - 14:42

buy cialis in the uk https://edpillsphrm.com how to order generic viagra

Отправил Impebra Сб, 04/25/2020 - 13:55

buy cheap viagra online uk generic ed pills order levitra online cod

Отправил HenryWaf Сб, 04/25/2020 - 13:45

viagra generic ed pills buy cialis in costa rica

Отправил Waltertib Сб, 04/25/2020 - 12:51

buy viagra goa generic viagra buy viagra hyderabad india

Отправил unrejerm Сб, 04/25/2020 - 12:47

buy name brand cialis online ed drugs online from canada buy cialis online legal

Отправил HenryWaf Сб, 04/25/2020 - 11:06

buy cialis online no prescription generic ed pills cheap viagra generic canada

Отправил Impebra Сб, 04/25/2020 - 11:02

cheap levitra professional oo https://edpillsphrm.com viagra gel for sale uk

Отправил Waltertib Сб, 04/25/2020 - 10:27

buy levitra us https://edpillsphrm.com generic levitra online cheap

Отправил unrejerm Сб, 04/25/2020 - 10:19

buy cialis and viagra online https://edpillsphrm.com order viagra online canada

Отправил HenryWaf Сб, 04/25/2020 - 08:16

where can i buy viagra in las vegas https://edpillsphrm.com buy viagra online cheap uk

Отправил Impebra Сб, 04/25/2020 - 08:05

viagra sale supermarkets list of approved canadian pharmacies how to order viagra in australia

Отправил Waltertib Сб, 04/25/2020 - 07:48

discount cialis in canada list of approved canadian pharmacies order generic cialis online

Отправил unrejerm Сб, 04/25/2020 - 07:45

buy cheap viagra online canada https://edpillsphrm.com viagra online order

Отправил HenryWaf Сб, 04/25/2020 - 05:08

viagra buy melbourne canada pharmacies online prescriptions can you buy viagra boots

Отправил unrejerm Сб, 04/25/2020 - 05:03

order cialis online overnight https://edpillsphrm.com order cialis at online pharmacy

Отправил Waltertib Сб, 04/25/2020 - 05:02

order levitra cheap https://edpillsphrm.com order cialis professional

Отправил Impebra Сб, 04/25/2020 - 04:58

buy cialis melbourne buy generic ed pills online viagra sale boots chemist

Отправил Ismaelbodia Сб, 04/25/2020 - 02:36

viagra canada https://viagrawithoutdoctorspres.com buy levitra pen

Отправил puboblix Сб, 04/25/2020 - 01:09

can buy viagra uk buy viagra viagra online generic cheap

Отправил unfoleror Сб, 04/25/2020 - 00:56

buy viagra yahoo answers buy viagra online buy viagra bangkok

Отправил Ismaelbodia Пт, 04/24/2020 - 23:51

cheapest pharmacy cialis buy generic viagra buy levitra online usa

Отправил Louischove Пт, 04/24/2020 - 23:50

buying cialis online in canada https://viagrawithoutdoctorspres.com download cheap viagra

Отправил unfoleror Пт, 04/24/2020 - 22:35

can buy cialis over counter usa buy viagra online order viagra boots

Отправил puboblix Пт, 04/24/2020 - 22:10

where can i buy viagra in london cheap viagra viagra buy no prescription canada

Отправил Ismaelbodia Пт, 04/24/2020 - 21:04

cheap viagra online uk cheap viagra order cialis online cheap

Отправил Louischove Пт, 04/24/2020 - 20:42

cheap viagra viagra for sale order viagra phone

Отправил unfoleror Пт, 04/24/2020 - 20:12

cialis 20 mg 4 tablet fiyat generic viagra online where can i buy viagra from

Отправил puboblix Пт, 04/24/2020 - 19:08

where to buy cialis in dubai viagra without prescription meds sale levitra

Отправил Ismaelbodia Пт, 04/24/2020 - 18:26

buy cialis drugstore viagra price where can i buy viagra online yahoo answers

Отправил unfoleror Пт, 04/24/2020 - 17:56

cheap viagra cialis uk buy generic viagra buy viagra forum

Отправил Louischove Пт, 04/24/2020 - 17:48

viagra for sale in new york buy generic viagra cheap cialis online pharmacy

Отправил Ismaelbodia Пт, 04/24/2020 - 16:11

how to cut cialis pills https://viagrawithoutdoctorspres.com viagra cheap online uk

Отправил puboblix Пт, 04/24/2020 - 16:07

viagra cialis levitra buy online generic viagra online cheapest cialis generic

Отправил unfoleror Пт, 04/24/2020 - 15:38

buy viagra doha viagra price purchase cialis online cheap

Отправил Louischove Пт, 04/24/2020 - 14:46

cialis cheap fast delivery https://viagrawithoutdoctorspres.com sales cheap generic viagra com

Отправил Ismaelbodia Пт, 04/24/2020 - 13:54

cheap viagra for women buy generic viagra where can i buy the viagra

Отправил unfoleror Пт, 04/24/2020 - 13:20

buy cialis daily use https://viagrawithoutdoctorspres.com generic cialis india

Отправил puboblix Пт, 04/24/2020 - 13:07

cheap viagra ireland https://viagrawithoutdoctorspres.com buy viagra boots uk

Последние комментарии

  • generic cialis no doctor's prescription https://cialmen.com prices of cialis buy viagra cialis order cialis cialis and interaction with ibutinib
  • Guys just made a web-page for me, look at the link: https://beachbags-11.webself.net/ Tell me your credentials. Thank you.
  • Guys just made a website for me, look at the link: http://ternogradu0.bloguetechno.com/--29077808 Tell me your prescriptions. Thanks.

Счетчики