答案
B

解:当P为AB上时,假设P为中点时,AP=PB=PC,满足条件,
当点P不为中点时,过点C作AB的垂线,亦满足条件;
当点P在BA的延长线上时,过点P作PF⊥BC,PE⊥CA;
PC
2=PF
2+CF
2,AP
2=AE
2+PE
2=AE
2+FC
2=2CF
2PB
2=BF
2+PF
2=PF
2+(BC+CF)
2=2PF
2AP
2+PB
2=2CF
2+PF
2+PF
22PC
2=2PF
2+2CF
2所以AP
2+PB
2=2PC
2,
即S=2CP
2;
同理,当点P在AB的延长线上时,S=2CP
2.
综上可知:S=2CP
2.
故选B.