In 2009, the 22 nd math problem in Wenzhou senior high school entrance examination was the second problem.
Add OE, because EF is the tangent of O radius.
So ∠ deo+∠ def = 90.
∠∠AEF+∠def = 90 ∴∠aef=∠aeo
∫△DBE∽△ABC ∴∠a=∠edb
∠∠edo =∠deo∴∠AEF =∠a
△ FAE is an isosceles triangle.