Acwing 4499. draw a circle (similar to a triangle)

Topic link ：4499. A circle - AcWing Question bank

In a two-dimensional plane , Give one with  (x1,y1)(x1,y1)  For the center of a circle , The radius is  RR  And a coordinate of  (x2,y2)(x2,y2)  The point of .

Please draw a circle on the two-dimensional plane , requirement ：

1. There is no point satisfaction in the plane, not only on the circle you draw , And outside the given circle .
2. The given point cannot be in the circle you draw （ Can be on a circle ）.
3. The area covered by the given circle and not covered by the circle you draw should be as small as possible .

Please output the center coordinates and radius of the circle you drew .

Input format

All in one line , contain  55  It's an integer  R,x1,y1,x2,y2R,x1,y1,x2,y2.

Output format

Three real numbers  xans,yans,rxans,yans,r, among  (xans,yans)(xans,yans)  Is the coordinate of the center of the circle you drew ,rr  Is the radius of the circle you drew .

Keep the result to six decimal places .

Data range

All test points meet  1≤R≤1051≤R≤105,|x1|,|y1|,|x2|,|y2|≤105|x1|,|y1|,|x2|,|y2|≤105.

sample input 1：

5 3 3 1 1

sample output 1：

3.767767 3.767767 3.914214

sample input 2：

10 5 5 5 15

sample output 2：

5.000000 5.000000 10.000000

Code ：

#include<bits/stdc++.h>  //  Similar triangles 
using namespace std;
#define endl "\n"


int main() {
    ios::sync_with_stdio(false);
    cout.tie(0);

    double r, x1, x2, y1, y2;
    cin >> r >> x1 >> y1 >> x2 >> y2;

    if(sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)) >= r) {   //  Outside the circle 
        cout << fixed << setprecision(6) << x1 << " " << y1 << " " << r;
    } else {                                                         //  In a circle 
        if(x1 == x2 && y1 == y2) {                                    //  In coincidence 
           double rr = r / 2.0;
           x2 += rr;
           cout << fixed << setprecision(6) << x2 << " " << y2 << " " << rr;
        }
        else {                                                      //  When they don't coincide 
             double len = sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
             double rr = len + r;
                rr /= 2.0;
                x2 += rr * (x1 - x2) / len;     // (x1 - x2) / len = cos
                y2 += rr * (y1 - y2) / len;     // (y1 - y2) / len = sin
                cout << fixed << setprecision(6) << x2 << " " << y2 << " " << rr;
        }
    }

    return 0;
}