triangulo.cpp

template <typename T>
struct Triangle {
  Point<T> A, B, C;

  // Definição do método area()

  // circulo inscrito no triangulo
  double circumradius() const {
    auto a = dist(B, C);
    auto b = dist(A, C);
    auto c = dist(A, B);

    return (a * b * c) / (4 * area());
  }

  Point<T> circumcenter() const {
    auto D = 2 * (A.x * (B.y - C.y) + B.x * (C.y - A.y) + C.x * (A.y - B.y));

    auto A2 = A.x * A.x + A.y * A.y;
    auto B2 = B.x * B.x + B.y * B.y;
    auto C2 = C.x * C.x + C.y * C.y;

    auto x = (A2 * (B.y - C.y) + B2 * (C.y - A.y) + C2 * (A.y - B.y)) / D;
    auto y = (A2 * (C.x - B.x) + B2 * (A.x - C.x) + C2 * (B.x - A.x)) / D;

    return {x, y};
  }

  // ortocentro do triangulo
  Point<T> orthocenter() const {
    Line<T> r(A, B), s(A, C);

    Line<T> u{r.b, -r.a, -(C.x * r.b - C.y * r.a)};
    Line<T> v{s.b, -s.a, -(B.x * s.b - B.y * s.a)};

    auto det = u.a * v.b - u.b * v.a;
    auto x = (-u.c * v.b + v.c * u.b) / det;
    auto y = (-v.c * u.a + u.c * v.a) / det;

    return {x, y};
  }
};