Circle vs pie segment collision detection

[User137]

With functions in my lib:

// Angle between 2 vectors, given in radians
function Angle(src,dest: single): single;
begin
  result:=src-dest;
  while result<-PI do result:=result+PI*2;
  while result>PI do result:=result-PI*2;
end;

// By pythagoras a^2+b^2=c^2 you don't need Sqrt() to determine the equality
function PointInCircle(const p,circle: TVector2f; const radius: single): boolean;
var x,y: single;
begin
  x:=circle.x-p.x; y:=circle.y-p.y;
  PointInCircle:=(x*x+y*y)<(radius*radius);
end;

And knowing the angle_delta that is half of pie's slice angle, we can count if point is between them:

if PointInCircle(beam.position, player.position, radius) then
  if abs(Angle(beam.angle, angle_from_beam_to_player)) < angle_delta then begin
    Collide;
  end;

You can also use this for the angle from beam to player:

function Angle(const px1,py1,px2,py2: single): single;
begin
  result:=arctan2(py2-py1,px2-px1);
  if result<0 then result:=result+PI*2;
end;