Circles of given radius through two points

From Rosetta Code
Circles of given radius through two points is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given two points on a plane and a radius, at most two circles of given radius can be drawn through the points.

  1. Write a function/subroutine/method/... that takes two points and a radius and returns the circles through those points.
  2. Show here the output for the following inputs:
      p1                p2           r
0.1234, 0.9876    0.8765, 0.2345    2.0
0.1234, 0.9876    0.1234, 0.9876    2.0
0.1234, 0.9876    0.8765, 0.2345    0.5
Ref

Python

This example is incorrect. It does not accomplish the given task. Please fix the code and remove this message.

<lang 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'
   (x1, y1), (x2, y2) = p1, p2
   if p1 == p2:
       return Cir(x1, y1, r), Cir(x1, y1, r)
   # delta x, delta y between points
   dx, dy = x2 - x1, y2 - y1
   # dist between points
   q = sqrt(dx**2 + dy**2)
   if q > 2.0*r:
       # raise ValueError('separation of points > diameter')
       return None, None
   # halfway point
   x3, y3 = (x1+x2)/2, (y1+y2)/2
   # distance along the mirror line
   d = sqrt(r**2-(q/2)**2)
   # One answer
   c1 = Cir(x = x3 - d*dy/q,
            y = y3 + d*dx/q,
            r = abs(r))
   # The other answer
   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(0.1234, 0.9876), Pt(0.1234, 0.9876), 2.0),
                     (Pt(0.1234, 0.9876), Pt(0.8765, 0.2345), 0.5)]:
       print('Through points:\n  %r,\n  %r\n  and radius %f\nYou can construct the following circles:'
             % (p1, p2, r))
       print('  %r\n  %r\n' % circles_from_p1p2r(p1, p2, r))</lang>
Output:
Through points:
  Pt(x=0.1234, y=0.9876),
  Pt(x=0.8765, y=0.2345)
  and radius 2.000000
You can construct the following circles:
  Circle(x=1.8631118016581893, y=1.974211801658189, r=2.0)
  Circle(x=-0.8632118016581896, y=-0.7521118016581892, r=2.0)

Through points:
  Pt(x=0.1234, y=0.9876),
  Pt(x=0.1234, y=0.9876)
  and radius 2.000000
You can construct the following circles:
  Circle(x=0.1234, y=0.9876, r=2.0)
  Circle(x=0.1234, y=0.9876, r=2.0)

Through points:
  Pt(x=0.1234, y=0.9876),
  Pt(x=0.8765, y=0.2345)
  and radius 0.500000
You can construct the following circles:
  None
  None
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