Connecting BI

∵I is the heart of △ABC.

∴∠BAI=∠CAI，ABI = CBI。 Arc BD= arc CD.

∴∠BAD =∠DBC

∠∠BID =∠BAI+∠ABI

∠IBD=∠IBC +∠DBC

∴∠DBI=∠DIB

∴DB =DI