Найти точки, которые принадлежат области пересечения - Prolog

%?radius ?X ?Y
:-dynamic
    circle/3.
initial_db:-
    circle(_,_,_),!.
initial_db:-
    assert(circle(2,1,1)),
    assert(circle(4,1,3)),
    assert(circle(1,3,1)),
    assert(circle(5,1,5)),
    assert(circle(3,5,1)),
    assert(circle(2,3,3)).

%?Name ?X ?Y
:-dynamic
    point/3.
initial_db:-
    point(_,_,_),!.
initial_db:-
    assert(point(a,1,1)),
    assert(point(b,1,3)),
    assert(point(c,3,1)),
    assert(point(d,1,5)),
    assert(point(e,5,1)),
    assert(point(f,3,3)).
 
% ?R1 ?X1 ?Y1 ?R2 ?X2 ?Y2 -List of possible points
all_points(R1,X1,Y1,R2,X2,Y2,ResultList):-
    findall(point : P, is_intersect(R1,X1,Y1,R2,X2,Y2,P), ResultList).
    
% ?R1 ?X1 ?Y1 ?R2 ?X2 ?Y2
is_intersect(R1,X1,Y1,R2,X2,Y2,P):-
    point(P,X,Y),
    check_insert(R1,X1,Y1,X,Y),
    check_insert(R2,X2,Y2,X,Y).
 
% ?R ?X1 ?Y1 ?PX ?PY
check_insert(R,X,Y,PX,PY):-
    D is sqrt((PX-X)*(PX-X) + (PY-Y)*(PY-Y)),
    D < R.