连接A、B，AB：
y=kx+b k=(y₂-y₁)/(x₂-x₁),b=(x₂y₁-x₁y₂)/(x₂-x₁)
x²+(kx+b)²=4→(1+k²)x²+2kbx+b²-4=0
x₁·x₂=(b²-4)/(1+k²)
y₁·y₂=(kx₁+b)(kx₂+b)=(b²-4)k²/(1+k²)+bk(x₁+x₂)+b²
=(b²-4k²)/(1+k²)
x₁·x₂+y₁·y₂=(b²-4)/(1+k²)+(b²-4k²)/(1+k²)=-2
b²=k²+1→b=±√(1+k²)
x₁+x₂+y₁+y₂=x₁+x₂+kx₁+b+kx₂+b
=(1+k)(x₁+x₂)+2b
=(1+k)(-2kb)/(1+k²)+2b
=2b-(2k+2k²)/b
可求得k=-1(b=-√2)时，取得最小值=-2√2
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