luofeng8823
花朵
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显然圆心M在的AB中垂线x = y上
M(m,m)
(x - m)² + (y - m)² = OM² = 2m²
⊙M过A(a,0):(a - m)² + m² = 2m²
m = a/2
M(a/2,a/2),r² = OM² = a²/2
M与直线x+y-2=0的距离h = |a/2 + a/2 - 2|/√2 = |a - 2|/√2
半弦长为d = √(r² - h²) = √[a²/2 - (a - 2)²/4]
弦长2d = 2√[a²/2 - (a - 2)²/4] = √(a² + 4a - 4)
于是从弦长可以解出a
1年前
8