如图,在△ABC中,∠ABC=90°,PA⊥平面ABC于点A,AM⊥PC于点M,AN⊥PB于点N,连结MN

(1)∵PA⊥平面ABC,∴PA⊥BC,又BC⊥AB,∴BC⊥平面PAB,∴BC⊥AN,又AN⊥PB,∴AN⊥平面PBC,又平面AMN经过AN,∴平面AMN⊥平面PBC.
(2)∵AN⊥平面PBC,∴AN⊥PC,又PC⊥AM,∴PC⊥平面AMN,∴MN⊥PC.