Task: Circles of given radius through two points
C++: #include <iostream>
#include <cmath>
#include <tuple>

struct point { double x, y; };

bool operator==(const point& lhs, const point& rhs)
{ return std::tie(lhs.x, lhs.y) == std::tie(rhs.x, rhs.y); }

enum result_category { NONE, ONE_COINCEDENT, ONE_DIAMETER, TWO, INFINITE };

using result_t = std::tuple<result_category, point, point>;

double distance(point l, point r)
{ return std::hypot(l.x - r.x, l.y - r.y); }

result_t find_circles(point p1, point p2, double r)
{
    point ans1 { 1/0., 1/0.}, ans2 { 1/0., 1/0.};
    if (p1 == p2) {
        if(r == 0.) return std::make_tuple(ONE_COINCEDENT, p1,   p2  );
        else        return std::make_tuple(INFINITE,       ans1, ans2);
    }
    point center { p1.x/2 + p2.x/2, p1.y/2 + p2.y/2};
    double half_distance = distance(center, p1);
    if(half_distance > r)      return std::make_tuple(NONE,         ans1,   ans2);
    if(half_distance - r == 0) return std::make_tuple(ONE_DIAMETER, center, ans2);
    double root = std::hypot(r, half_distance) / distance(p1, p2);
    ans1.x = center.x + root * (p1.y - p2.y);
    ans1.y = center.y + root * (p2.x - p1.x);
    ans2.x = center.x - root * (p1.y - p2.y);
    ans2.y = center.y - root * (p2.x - p1.x);
    return std::make_tuple(TWO, ans1, ans2);
}

void print(result_t result, std::ostream& out = std::cout)
{
    point r1, r2; result_category res;
    std::tie(res, r1, r2) = result;
    switch(res) {
      case NONE:
        out << "There are no solutions, points are too far away\n"; break;
      case ONE_COINCEDENT: case ONE_DIAMETER:
        out << "Only one solution: " << r1.x << ' ' << r1.y << '\n'; break;
      case INFINITE:
        out << "Infinitely many circles can be drawn\n"; break;
      case TWO:
        out << "Two solutions: " << r1.x << ' ' << r1.y << " and " << r2.x << ' ' << r2.y << '\n'; break;
    }
}

int main()
{
    constexpr int size = 5;
    const point points[size*2] = {
        {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}
    };
    const double radius[size] = {2., 1., 2., .5, 0.};

    for(int i = 0; i < size; ++i)
        print(find_circles(points[i*2], points[i*2 + 1], radius[i]));
}

Go: package main

import (
    "fmt"
    "math"
)

var (
    Two  = "Two circles."
    R0   = "R==0.0 does not describe circles."
    Co   = "Coincident points describe an infinite number of circles."
    CoR0 = "Coincident points with r==0.0 describe a degenerate circle."
    Diam = "Points form a diameter and describe only a single circle."
    Far  = "Points too far apart to form circles."
)

type point struct{ x, y float64 }

func circles(p1, p2 point, r float64) (c1, c2 point, Case string) {
    if p1 == p2 {
        if r == 0 {
            return p1, p1, CoR0
        }
        Case = Co
        return
    }
    if r == 0 {
        return p1, p2, R0
    }
    dx := p2.x - p1.x
    dy := p2.y - p1.y
    q := math.Hypot(dx, dy)
    if q > 2*r {
        Case = Far
        return
    }
    m := point{(p1.x + p2.x) / 2, (p1.y + p2.y) / 2}
    if q == 2*r {
        return m, m, Diam
    }
    d := math.Sqrt(r*r - q*q/4)
    ox := d * dx / q
    oy := d * dy / q
    return point{m.x - oy, m.y + ox}, point{m.x + oy, m.y - ox}, Two
}

var td = []struct {
    p1, p2 point
    r      float64
}{
    {point{0.1234, 0.9876}, point{0.8765, 0.2345}, 2.0},
    {point{0.0000, 2.0000}, point{0.0000, 0.0000}, 1.0},
    {point{0.1234, 0.9876}, point{0.1234, 0.9876}, 2.0},
    {point{0.1234, 0.9876}, point{0.8765, 0.2345}, 0.5},
    {point{0.1234, 0.9876}, point{0.1234, 0.9876}, 0.0},
}

func main() {
    for _, tc := range td {
        fmt.Println("p1: ", tc.p1)
        fmt.Println("p2: ", tc.p2)
        fmt.Println("r: ", tc.r)
        c1, c2, Case := circles(tc.p1, tc.p2, tc.r)
        fmt.Println("  ", Case)
        switch Case {
        case CoR0, Diam:
            fmt.Println("   Center: ", c1)
        case Two:
            fmt.Println("   Center 1: ", c1)
            fmt.Println("   Center 2: ", c2)
        }
        fmt.Println()
    }
}