Best way to find a point on a circle closest to a given point

V = (P - C); Answer = C + V / |V| * R;

double vX = pX - cX;
double vY = pY - cY;
double magV = sqrt(vX*vX + vY*vY);
double aX = cX + vX / magV * R;
double aY = cY + vY / magV * R;

m=(cY-pY)/(cX-pX);  //slope
b=cY-m*cX;  //or Py-m*Px.  Now you have a line in the form y=m*x+b
X=(  (2mcY)*((-2*m*cY)^2-4*(cY^2+cX^2-b^2-2*b*cY-r^2)*(-1-m^2))^(1/2)  )/(2*(cY^2+cX^2-b^2-2*bc*Y-r^2));
Y=mX+b;