#include<stdio.h>
#include<iostream.h>
#include<math.h>
#include<conio.h>
 typedef struct punct{
	int x,y;
 }punct;
 typedef struct punctreal{
	//centrul cercului circumscris
	double x,y;
 }punctreal;
 punct a,b,c;
 punctreal O;//centrul cercului
 double r;
 void citire_triunghi(){
	printf("coordonatele punctului A sunt:");
	scanf("%d %d",&a.x,&a.y);
	printf("coordonatele punctului B sunt:");
	scanf("%d %d",&b.x,&b.y);
	printf("coordonatele punctului C sunt:");
	scanf("%d %d",&c.x,&c.y);
 }
 void desenare_triunghi(punct a, punct b, punct c){
        moveto(a.x,a.y);
        setcolor(BLUE);
        line(a.x,a.y,b.x,b.y);
        line(b.x,b.y,c.x,c.y);
        line(c.x,c.y,a.x,a.y);
        setcolor(RED);
        outtextxy(a.x,a.y,"A");
        outtextxy(b.x,b.y,"B");
        outtextxy(c.x,c.y,"C");
 }
 punctreal centru_cerc(punct a, punct b,punct c){
	punctreal centru;
	double D,Dm,Dn;
	D=(double)(b.x-a.x)*(c.y-a.y)-(double)(b.y-a.y)-(c.x-a.x);
	D=-4*D;
	Dm=(pow(a.x,2)+pow(a.y,2))*(b.y-c.y)+(pow(b.x,2)+pow(b.y,2))*(c.y-a.y)+(pow(c.x,2)+pow(c.y,2))*(a.y-b.y);
	Dm=-2*Dm;
	Dn=(pow(a.x,2)+pow(a.y,2))*(b.x-c.x)+(pow(b.x,2)+pow(b.y,2))*(c.x-a.x)+(pow(c.x,2)+pow(c.y,2)0*(a.x-b.x);
	Dn=2*Dn;
	if(D==0)
		printf("puncte coliniare");
	else{
		centru.x=Dm/D;
		centru.y=Dn/D;
	}
	return centru;
 }
 double raza_cerc(punct a,punct b,punct c){
	punctreal centru;
	double raza;
	centru=centru_cerc(a,b,c);
	raza=sqrt((centru.x-a.x)*(centru.x-a.x)+(centru.y-a.y)*(centru.y-a.y));
	return raza;
 }
 double distanta(punct p, punct q){
	 return sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2));
 }
 punctreal centrucercinscris(punct A,punct B, punct C){
	double a=distanta(B,C);
	double b=distanta(A,C);
	double c=distanta(A,B);
	double p=a+b+c;
	punctreal centru;
	centru.x=A.x*a/p+B.x*b/p+C.x*c/p;
	centru.y=A.y*a/p+B.y*b/p+C.y*c/p;
	return centru;
 }
 double razacercinscris(punct A,punct B,punct C){
        double a=distanta(B,C);
	double b=distanta(A,C);
	double c=distanta(A,B);
	double p=a+b+c/2;
        double S=fabs(((double)(B.x-A.x)*(C.y-A.y)-(double)(B.y-A.y)*(C.x-A.x))/2);
        double raza=S/p;
        return raza;
 }
 void main(){
        punctreal I;
        double R;
        int gd=DETECT,gm;
        citire_triunghi();
        initgraph(&gd,&gm,"C:\\tc\\BGI");
        desenare_triunghi(a,b,c);
        O=centru_cerc(a,b,c);
        r=raza_cerc(a,b,c);
        setcolor(RED);
        circle(O.x,O.y);//deseneaza cercul de raza r circumscris
        setcolor(RED); circle(O.x,O.y,1);
        I=centrucercinscris(a,b,c);
        R=razacercinscris(a,b,c);
        setcolor(GREEN);
        circle(I.x,I.y,R);//deseneaza cercul de raza R inscris
        setcolor(GREEN);circle(I.x,I.y,1);
        getch();
        closegraph();
 }