折腾了半天，没想出怎么证明，以前初中老师教过，不知道怎么办，就量量。。。受不了，怒抄模版1Y。。。
1 #include <cstdio> 2 #include <iostream> 3 using namespace std; 4 #define eps 1e-8 5 struct point 6 { 7 double x,y; 8 }; 9 struct line 10 { 11 point a,b; 12 }; 13 point intersection(line u,line v) 14 { 15 point ret = u.a; 16 double t = ((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x)) 17 /((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x)); 18 ret.x += (u.b.x-u.a.x)*t; 19 ret.y += (u.b.y-u.a.y)*t; 20 return ret; 21 } 22 point perpencenter(point a,point b,point c) 23 { 24 line u,v; 25 u.a = c; 26 u.b.x = u.a.x - a.y + b.y; 27 u.b.y = u.a.y + a.x - b.x; 28 v.a = b; 29 v.b.x = v.a.x - a.y + c.y; 30 v.b.y = v.a.y + a.x - c.x; 31 return intersection(u,v); 32 } 33 int main() 34 { 35 int t; 36 point a,b,c; 37 scanf("%d",&t); 38 while(t--) 39 { 40 scanf("%lf%lf%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y,&c.x,&c.y); 41 a = perpencenter(a,b,c); 42 printf("%.4f %.4f ",a.x+eps,a.y+eps); 43 } 44 return 0; 45 }