∵⊙O is the circumscribed circle of Rt△ACB, and ∠C is a right angle.

∴AB is the diameter

AB = 4，BC=2

∴∠BAC=30？

∵ equilateral triangle△ △ACD

So ∠CAD=60?

Bad = 90 means da ∴ ba.

Ab is the diameter.

∴。 .。 . . Tangent to ...

2.AE=3

Point e is on the circle and AB is the diameter.

∴∠BEA=90？

AC=2√3 can be obtained from Rt△ACB.

AD=2√3 can be obtained from equilateral △ACD.

In Rt△BAD, BD=2√7.

∵AE⊥BD？ ,? BA⊥DA

According to photography theorem, AB? = be BD, then BE=√7.

In Rt△BEA, BE=√7 and AB=4.

∴AE=3