Reason: Making friends with AQ⊥AP and ⊿ABC≌⊿ADE is asking a question.

∴ ∠ABP=∠ACP

And because AC=AC and it is easy to prove ∠BAQ=∠CAP,

∴ ⊿APC≌⊿AQB

∴CP=BQ

And ∵ BQ-PB=PQ=√2PA.

∴PC-PB=√2PA