Prove that BFCE is a cyclic quadrilateral, given that FBC = 90^

We are given that $\angle FBC = 90^\circ$.
To prove that BFCE is a cyclic quadrilateral, we need to show that the sum of its opposite angles is $180^\circ$. Specifically, we need to show that $\angle FBC + \angle FEC = 180^\circ$. Since $\angle FBC = 90^\circ$, we must prove that $\angle FEC = 90^\circ$.

Points A, F, G, B lie on the first circle