问题
填空题
设A为圆周上的一个定点,在圆周上随机取一点与A连接,则弦长超过半径的概率为______.
答案
在圆上其他位置任取一点B,设圆半径为R,
则B点位置所有情况对应的弧长为圆的周长2πR,
其中满足条件AB的长度大于等于半径长度的对应的弧长为
•2πR,2 3
则AB弦的长度大于等于半径长度的概率P=
=
•2πR2 3 2πR 2 3
故答案为:2 3
设A为圆周上的一个定点,在圆周上随机取一点与A连接,则弦长超过半径的概率为______.
在圆上其他位置任取一点B,设圆半径为R,
则B点位置所有情况对应的弧长为圆的周长2πR,
其中满足条件AB的长度大于等于半径长度的对应的弧长为
•2πR,2 3
则AB弦的长度大于等于半径长度的概率P=
=
•2πR2 3 2πR 2 3
故答案为:2 3
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