Because I am the heart, BAE = EAC, BCI = ACI.

Because the circumferential angles of the same arc are equal,

So ∠EBC=∠EAC, ∠BAE=∠BCE,

So ∠EBC=∠BCE, so BE=CE.

Because EIC = IAC+ICA and ECI = ECB+ICD.

So ∠EIC=∠ECI, so EI=EC.

So BE=CE= EI