#include <bits/pthreadtypes.h>
#include <float.h>
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

#ifdef __PROGTEST__
#define debug(...) ((void)0)
#else
#define debug(fmt, ...)                                                        \
  fprintf(stdout, "[%s:%d %s()] " fmt "\n", __FILE__, __LINE__, __func__,      \
          ##__VA_ARGS__)
#endif

double clamp(double d) {
  if (d > 1.0) {
    return 1.0;
  } else if (d < -1.0) {
    return -1.0;
  } else {
    return d;
  }
}

// https://www.geeksforgeeks.org/dsa/area-of-intersection-of-two-circles/
double intersection_area(double a_r, double b_r, double distance) {
  double a_square = a_r * a_r;
  double b_square = b_r * b_r;
  double distance_square = distance * distance;

  double alpha_acos =
      (distance_square + a_square - b_square) / (2 * a_r * distance);
  double beta_acos =
      (distance_square + b_square - a_square) / (2 * b_r * distance);

  double alpha = acos(clamp(alpha_acos)) * 2;
  double beta = acos(clamp(beta_acos)) * 2;

  double a1 = 0.5 * beta * b_square - 0.5 * b_square * sin(beta);
  double a2 = 0.5 * alpha * a_square - 0.5 * a_square * sin(alpha);

  double area = a1 + a2;

  debug("Area = %lf", area);

  return area;
}

double circle_area(double radius) { return M_PI * radius * radius; }

int main() {
  double a_center_x = 0, a_center_y = 0, a_radius = 0, b_center_x = 0,
         b_center_y = 0, b_radius = 0;

  printf("Zadejte parametry kruznice #1:\n");

  int inputs_read = scanf("%lf %lf %lf", &a_center_x, &a_center_y, &a_radius);
  if (inputs_read != 3 || a_radius <= 0) {
    printf("Nespravny vstup.\n");
    return EXIT_FAILURE;
  }

  printf("Zadejte parametry kruznice #2:\n");

  inputs_read = scanf("%lf %lf %lf", &b_center_x, &b_center_y, &b_radius);
  if (inputs_read != 3 || b_radius <= 0) {
    printf("Nespravny vstup.\n");
    return EXIT_FAILURE;
  }

  double center_distance =
      sqrt((b_center_x - a_center_x) * (b_center_x - a_center_x) +
           (b_center_y - a_center_y) * (b_center_y - a_center_y));

  debug("Distance of centers = %0.60lf", center_distance);
  debug("Radii difference = %0.60lf", a_radius - b_radius);
  debug("Radii difference = %0.60lf", b_radius - a_radius);
  debug("Center + #1 = %0.60lf", a_center_x + a_radius);
  debug("Center + #2 = %0.60lf", b_center_x + b_radius);

  double radii_sum = a_radius + b_radius;
  double radii_difference = fabs(a_radius - b_radius);
  double epsilon = 100 * DBL_EPSILON * fmax(a_radius, b_radius);

  // Both origin points and radii are identical
  bool are_identical = a_center_x == b_center_x && a_center_y == b_center_y && a_radius == b_radius;

  // d = r1 + r2
  // d - r1 - r1 < epsilon
  bool are_touching_from_outside = fabs(center_distance - radii_sum) < epsilon;

  // d = |r1 - r2|
  // d - |r1 - r2| < epsilon
  bool are_touching_from_inside = fabs(center_distance - radii_difference) < epsilon;

  // d < |r1 - r2|
  bool is_fully_inside = center_distance < radii_difference;

  // d < r1 + r2
  bool are_overlapping = center_distance < radii_sum;

  if (are_identical) {
    printf("Kruznice splyvaji, prekryv: %lf\n", circle_area(a_radius));
  }
  else if (are_touching_from_inside) {
    if (a_radius > b_radius) {
      printf(
          "Vnitrni dotyk, kruznice #2 lezi uvnitr kruznice #1, prekryv: %lf\n",
          circle_area(b_radius));
    } else {
      printf(
          "Vnitrni dotyk, kruznice #1 lezi uvnitr kruznice #2, prekryv: %lf\n",
          circle_area(a_radius));
    }
  }
  else if (are_touching_from_outside) {
    printf("Vnejsi dotyk, zadny prekryv.\n");
  }
  else if (is_fully_inside) {
    if (a_radius > b_radius) {
      printf("Kruznice #2 lezi uvnitr kruznice #1, prekryv: %lf\n",
             circle_area(b_radius));
    } else {
      printf("Kruznice #1 lezi uvnitr kruznice #2, prekryv: %lf\n",
             circle_area(a_radius));
    }
  }
  else if (are_overlapping) {
    printf("Kruznice se protinaji, prekryv: %lf\n",
           intersection_area(a_radius, b_radius, center_distance));
  }
  else {
    printf("Kruznice lezi vne sebe, zadny prekryv.\n");
  }

  return EXIT_SUCCESS;
}