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 ~