title: How to calculate (x,y) for a fixed arc length away from a point on a circumference
body: <p>I've spent so many hours on this I can feel my sanity slowly slipping. So any help would be really truly appreciated.
  I'll try and be as succinct as possible.</p>
  
  <p>I have a circle on a 2D plane. I know the cartesian coordinates for it's central point(C) and the radius(R).</p>
  
  <p>My confusion stems from this problem. When provided with a point on the plane outside of the circle; I can calculate the point(P) on the circle's circumference closest to that point.</p>
  
  <p>What I want to do is determine the (x,y) coordinates of 2 points on the circumference. Let's call them P1 and P2. P1 and P2 are two ends of an arc. The arc is of a fixed length(X). P is the midway point between P1 and P2. As such, the arc length from P to P1 &amp; P to P2 are both X/2.</p>
  
  <p>In short:
  given C, R, P, X ; I need to calculate P1 and P2.</p>
  
  <p>I am trying to code this in c++ but any suggestions or pseudo-code would be great.</p>
  
  <p>EDIT:
  X is an arc length, not a straight line between P1 and P2</p>