Rotate AP 60 degrees clockwise around point A and extend to point D, so that AD=2AP. Connecting BD, DB, PP', easy to prove: △APC? △ ADB,

Get ∠ APC = ∠ ADB = 120, BD-2pc, and prove ∠ APD = 90 by the middle line of one side of the triangle.

DP=3, so ∠ ADP = 30, ∠ BDP = 90, BD=4, so BD=4, thus obtaining the PC length.