如圖1,在矩形ABCD中,AB=6cm,BC=8cm,點(diǎn)P以3cm/s的速度從點(diǎn)A向點(diǎn)B運(yùn)動(dòng),點(diǎn)Q以4cm/s的速度從點(diǎn)C向點(diǎn)B運(yùn)動(dòng).點(diǎn)P、Q同時(shí)出發(fā),運(yùn)動(dòng)時(shí)間為t秒(0<t<2),⊙M是△PQB的外接圓.
(1)當(dāng)t=1時(shí),⊙M的半徑是
cm,⊙M與直線CD的位置關(guān)系是
相離
相離
;
(2)在點(diǎn)P從點(diǎn)A向點(diǎn)B運(yùn)動(dòng)過程中.
①圓心M的運(yùn)動(dòng)路徑長(zhǎng)是
5
5
cm;
②當(dāng)⊙M與直線AD相切時(shí),求t的值.
(3)連接PD,交⊙M于點(diǎn)N,如圖2,當(dāng)∠APD=∠NBQ時(shí),求t的值.