So angle BAE= angle CAE and angle ABI= angle IBC.

And because angle BEA= angle BCA (two angles face the same arc)

Therefore, the angle ABE= the angle ADC (the sum of the internal angles of the triangle = 180).

Obviously, angle IBD+ angle BID= angle ADC.

Angle ADC- Angle IBC= Angle ABE- Angle ABI

So angel ·IBE = angel ·BIE

Isosceles triangle ~