title: Tangent circle(s) for two other circles?
body: <p>There are two circles: <strong>a</strong> centered at point <strong>A</strong>, and circle <strong>b</strong> (center at <strong>B</strong>). What is the equation to calculate 2D position of all or none tangent circles possible. Main constraint is, that radius is the same for all the circles. As far as I know, there should be either no solution (figure 2), or 2 solutions (figure 1). How to find out <em>if there are solutions</em>, and also <em>position of centers</em> of those solutions (<strong>C</strong> and <strong>D</strong>).</p>
  
  <p><img src="https://i.stack.imgur.com/NRSan.png" alt="enter image description here">
  <em>Figure 1</em>: 2 solutions should be possible here </p>
  
  <hr>
  
  <p><img src="https://i.stack.imgur.com/cybnL.png" alt="enter image description here">
  <em>Figure 2</em>: No solutions!</p>
  
  <p><strong>Update (solution):</strong></p>
  
  <p>1) Calculate distance from A to B -> <strong>|AB|</strong>:</p>
  
  <p><img src="https://i.stack.imgur.com/9mfUe.gif" alt="enter image description here"></p>
  
  <p>2) Checks whether a solution exist, it exist only if:</p>
  
  <p><img src="https://i.stack.imgur.com/g16Oh.gif" alt="enter image description here"></p>
  
  <p>3) If it exist, calculate half-point between points <strong>A</strong> and <strong>B</strong>:</p>
  
  <p><img src="https://i.stack.imgur.com/R4EJA.gif" alt="enter image description here"></p>
  
  <p>4) Create normalized perpendicular vector to line segment <strong>AB</strong>:</p>
  
  <p><img src="https://i.stack.imgur.com/bgPtm.gif" alt="enter image description here"></p>
  
  <p>5) Calculate distance from this H point to C point -> <strong>|HC|</strong>:</p>
  
  <p><img src="https://i.stack.imgur.com/Sy2Pc.gif" alt="enter image description here"></p>
  
  <p>6) Finally calculate point <strong>C</strong> along the (HC) starting at X at distance |HC|:</p>
  
  <p><img src="https://i.stack.imgur.com/BzKQO.gif" alt="enter image description here"></p>