在平面几何中(如图1),我们知道“直径所对的圆周角为直角”.即M为⊙C上的动点,总有MA·MB=0为定值.起点⊙C圆周上的向量称为⊙C的圆周向量.图1图2定理设⊙C的半径为R,其同心圆⊙C′的半径为R′,RR′,M是⊙C上的动点,AB是⊙C′的任一直径(如图2),那么MA·MB=R2-R′2为定值.证不 In plane geometry (see Figure 1), we know that “the diameter of the circle is the right angle.” That is, M is the moving point on ⊙C, there is always MA·MB=0 as the fixed value. The starting point ⊙C on the circumference The vector is called the circumstantial vector of ⊙C. Fig.1 Fig.2 The theorem Let 半径C be the radius of R, the radius of its concentric circle ′C’ is R’,RR’,M is the moving point on ⊙C,AB is ⊙C The diameter of any of the ’(Figure 2), then MA MB = R2-R’2 is a fixed value.