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如图所示,菱形ABCD的顶点A、B在x轴上,点A在点B的左侧,点D在y轴的正半轴上,∠BAD=60°,点A的坐标为(-2,0).

(1)求线段AD所在直线的函数表达式.
(2)动点P从点A出发,以每秒2个单位长度的速度,按照A→D→C→B的顺序在菱形的边上匀速运动,设运动时间为t秒.求t为何值时,以点P为圆心、以1为半径的圆与对角线AC相切?

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答案(点此获取答案解析)

(1)∵点A的坐标为(-2,0),∠BAD=60°,∠AOD=90°,
∴OD=OA?tan60°=2,
∴点D的坐标为(0,2),
设直线AD的函数表达式为y=kx+b,-2k+b=0;b=2,解得k=,b=2。
∴直线AD的函数表达式为y=x+2。

(2)∵四边形ABCD是菱形,
∴∠DCB=∠BAD=60°,

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