If ad ^ 2 = AE * AC, CD = CB

If ad ^ 2 = AE * AC, CD = CB

No picture!
Conjecture:
If AD & # 178; = AE * AC, CD = CB
prove:
∵AD²=AE×AC
∴AE:AD=AD:AC
For △ ACD and △ ade, a is the common angle
So △ ACD ∽ ade (edge)
That is to say, ∠ ADB = ∠ ACD
Ψ arc AB = arc ad (equal circle angles)
The diameter AC is the perpendicular of the chord BD
∴CD=CB