Uva 11152 Solution

Hints 1 :: 

https://math.stackexchange.com/questions/1582061/finding-the-radius-of-a-circle-inside-of-a-triangle/1582067#:~:text=use%20the%20fact%20that%20the,valid%20for%20a%20convex%20polygon..

Hints 2 :: 

https://www.mathopenref.com/trianglecircumcircle.html

#include<bits/stdc++.h>

using namespace std;

int main()

{

double a, b, c;

double pi = acos(-1);

ios_base :: sync_with_stdio;

cin.tie(NULL);

cout.tie(NULL);

while(cin >> a >> b >> c)

{

double s, triangel, circle1_area, circle2_area, r, R;

s = (a + b + c)/2.0;

triangel = sqrt(s*(s-a)*(s-b)*(s-c));

r = triangel/s;

circle1_area = pi * (r*r);

double d = (a+b+c) * (b+c-a) * (c+a-b) * (a+b-c);

R = (a * b * c) / sqrt(d);

circle2_area = pi * (R * R);

circle2_area = circle2_area - triangel;

triangel = triangel - circle1_area;

cout << showpoint;

cout << fixed;

cout << setprecision(4);

cout << circle2_area << " " << triangel << " " << circle1_area << "\n";

}

return 0;

}