直线x+2y+5=0与圆x2+y2=2相交于A,B两点,O为原点,则OA•OB=_.

问题描述:

直线x+2y+

5
=0与圆x2+y2=2相交于A,B两点,O为原点,则
OA
OB
=______.

圆心到直线的距离:

5
5
=1,则易知弦心距所在直线与AO的夹角是45°,则
OA
OB
=|
OA
|•
|OB
|cos90°=0

故答案为:0.