摘要：1． 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． ⑴求线段AD所在直线的函数表达式． ⑵动点P从点A出发.以每秒1个单位长度的速度.按照A→D→C→B→A的顺序在菱形的边上匀速运动一周.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? 答案:1 解:⑴∵点A的坐标为.∠BAD=60°.∠AOD=90°. ∴OD=OA·tan60°=. ∴点D的坐标为(0.).························································ 1分 设直线AD的函数表达式为. .解得. ∴直线AD的函数表达式为. ···································· 3分 ⑵∵四边形ABCD是菱形. ∴∠DCB=∠BAD=60°. ∴∠1=∠2=∠3=∠4=30°. AD=DC=CB=BA=4.···································································· 5分 如图所示: ①点P在AD上与AC相切时. AP1=2r=2. ∴t1=2. ·························································································· 6分 ②点P在DC上与AC相切时. CP2=2r=2. ∴AD+DP2=6. ∴t2=6. ··································· 7分 ③点P在BC上与AC相切时. CP3=2r=2. ∴AD+DC+CP3=10. ∴t3=10.··································· 8分 ④点P在AB上与AC相切时. AP4=2r=2. ∴AD+DC+CB+BP4=14. ∴t4=14. ∴当t=2.6.10.14时.以点P为圆心.以1为半径的圆与对角线AC相切. ······················································ 9分

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