a-c=(1-m,-n) ,b-c=(-m,1-n)
(a-c)*(b-c)=0===>-m(1-m)-n(1-n)=0===>m^2+n^2=m+n
点(m,n)到直线x+y+1=0的距离d=|m+n+1|/√2=|m^2+n^2+1|/√2>=|2mn+1|/√2
(当且仅当m=n时取到等号）此时m=n=0或m=n=1
m=n=0时dmin=√2/2
m=n=1时dmin=3√2/2