Finding a tangent vector from a given point and circle

oh hey, i know this.

live unity webgl demo here.

source code here.

core routine:

   // this approach is more geometrical and less algebraic than approach 1,
   // and far more stable. thanks to Mike Plotz for suggesting this direction.
   bool CircleTangents_2(Vector2 center, float r, Vector2 p, ref Vector2 tanPosA, ref Vector2 tanPosB) {
     p -= center;
     
     float P = p.magnitude;
     
     // if p is inside the circle, there ain't no tangents.
     if (P <= r) {
       return false;
     }
         
     float a = r * r                                          / P;    
     float q = r * (float)System.Math.Sqrt((P * P) - (r * r)) / P;
     
     Vector2 pN  = p / P;
     Vector2 pNP = new Vector2(-pN.y, pN.x);
     Vector2 va  = pN * a;
     
     tanPosA = va + pNP * q;
     tanPosB = va - pNP * q;
 
     tanPosA += center;
     tanPosB += center;
     
     return true;
   }
 

and finally a picture: