由圆外一点P(2,1)引圆O:x2+y2=4的割线交圆于A,B两点,求弦AB中点的轨迹.
题目
由圆外一点P(2,1)引圆O:x2+y2=4的割线交圆于A,B两点,求弦AB中点的轨迹.
答案
取O,P的中点C(1,1/2)设AB中点为M( x,y)
在RtΔOMP中,|MC|=1/2|OP|=√5/2=定长,所以M点的轨迹是圆
(x-1)^2+(y-1/2)^2=5/4
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