ADB =∠CDE

∴180-∠ a-∠ ADB =180-∠ e-∠ CDE means ∠ABD=∠ACE.

In △ABD and △ACP

∠A=∠E

AB=AC

∠ABD=∠ACE

∴△ABD≌△ACP(ASA)

∴BD=CP=2CE

∴CE=PE

At △BEC and △ BEP,

BE=EB

∠BEC=∠BEP

CE=PE

∴△BEC≌△BEP(SAS)

∴∠CBE=∠PBE

∴BD split equally ∠ABC