Task: Circles of given radius through two points
C: #include<stdio.h>
#include<math.h>

typedef struct{
	double x,y;
	}point;
	
double distance(point p1,point p2)
{
	return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}
	
void findCircles(point p1,point p2,double radius)
{
	double separation = distance(p1,p2),mirrorDistance;
	
	if(separation == 0.0)
	{
		radius == 0.0 ? printf("\nNo circles can be drawn through (%.4f,%.4f)",p1.x,p1.y):
							 printf("\nInfinitely many circles can be drawn through (%.4f,%.4f)",p1.x,p1.y);
	}
	
	else if(separation == 2*radius)
	{
		printf("\nGiven points are opposite ends of a diameter of the circle with center (%.4f,%.4f) and radius %.4f",(p1.x+p2.x)/2,(p1.y+p2.y)/2,radius); 
	}
	
	else if(separation > 2*radius)
	{
		printf("\nGiven points are farther away from each other than a diameter of a circle with radius %.4f",radius);
	}   
	
	else
	{
		mirrorDistance =sqrt(pow(radius,2) - pow(separation/2,2));
		
		printf("\nTwo circles are possible.");
		printf("\nCircle C1 with center (%.4f,%.4f), radius %.4f and Circle C2 with center (%.4f,%.4f), radius %.4f",(p1.x+p2.x)/2 + mirrorDistance*(p1.y-p2.y)/separation,(p1.y+p2.y)/2 + mirrorDistance*(p2.x-p1.x)/separation,radius,(p1.x+p2.x)/2 - mirrorDistance*(p1.y-p2.y)/separation,(p1.y+p2.y)/2 - mirrorDistance*(p2.x-p1.x)/separation,radius);
	}
}

int main()
{
    int i;

    point cases[] = 	
    {	{0.1234, 0.9876},    {0.8765, 0.2345},  
	{0.0000, 2.0000},    {0.0000, 0.0000},   
	{0.1234, 0.9876},    {0.1234, 0.9876},   
	{0.1234, 0.9876},    {0.8765, 0.2345},    
	{0.1234, 0.9876},    {0.1234, 0.9876}
    };

    double radii[] = {2.0,1.0,2.0,0.5,0.0};

    for(i=0;i<5;i++)
    {	
	printf("\nCase %d)",i+1);
	findCircles(cases[2*i],cases[2*i+1],radii[i]);
    }

    return 0;
}

Python: from collections import namedtuple
from math import sqrt

Pt = namedtuple('Pt', 'x, y')
Circle = Cir = namedtuple('Circle', 'x, y, r')

def circles_from_p1p2r(p1, p2, r):
    'Following explanation at http://mathforum.org/library/drmath/view/53027.html'
    if r == 0.0:
        raise ValueError('radius of zero')
    (x1, y1), (x2, y2) = p1, p2
    if p1 == p2:
        raise ValueError('coincident points gives infinite number of Circles')
    
    dx, dy = x2 - x1, y2 - y1
    
    q = sqrt(dx**2 + dy**2)
    if q > 2.0*r:
        raise ValueError('separation of points > diameter')
    
    x3, y3 = (x1+x2)/2, (y1+y2)/2
    
    d = sqrt(r**2-(q/2)**2)
    
    c1 = Cir(x = x3 - d*dy/q,
             y = y3 + d*dx/q,
             r = abs(r))
    
    c2 = Cir(x = x3 + d*dy/q,
             y = y3 - d*dx/q,
             r = abs(r))
    return c1, c2

if __name__ == '__main__':
    for p1, p2, r in [(Pt(0.1234, 0.9876), Pt(0.8765, 0.2345), 2.0),
                      (Pt(0.0000, 2.0000), Pt(0.0000, 0.0000), 1.0),
                      (Pt(0.1234, 0.9876), Pt(0.1234, 0.9876), 2.0),
                      (Pt(0.1234, 0.9876), Pt(0.8765, 0.2345), 0.5),
                      (Pt(0.1234, 0.9876), Pt(0.1234, 0.9876), 0.0)]:
        print('Through points:\n  %r,\n  %r\n  and radius %f\nYou can construct the following circles:'
              % (p1, p2, r))
        try:
            print('  %r\n  %r\n' % circles_from_p1p2r(p1, p2, r))
        except ValueError as v:
            print('  ERROR: %s\n' % (v.args[0],))