纯数学知识：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef struct circle
{
    int x, y, r;
}circle;


double distance(circle *A, circle *B){
    int dx = A->x-B->x;
    int dy = A->y-B->y;
    return sqrt(dx*dx + dy*dy);
}

int main() {
    int n;
    scanf("%d" ,&n);
    while(n--){
        circle A, B;
        scanf("%d %d %d", &A.x, &A.y, &A.r);
        scanf("%d %d %d", &B.x, &B.y, &B.r);
        double d = distance(&A, &B);
        if(d > (A.r + B.r)){
            printf("4\n");
        }
        else if (d == (A.r + B.r))
        {
            printf("3\n");
        }
        else if (d > abs(A.r - B.r)&& d < (A.r + B.r))
        {
            printf("2\n");
        }
        else if (d == abs(A.r - B.r))
        {
            printf("1\n");
        }
        else
        {
            printf("0\n");
        }
    }
    return 0;
}