Answer
Since all three sides are congruent, $~~\triangle AOF \cong \triangle AOE~~$ by SSS
Work Step by Step
We can show that the three sides of the triangles are congruent.
$OF \cong OE$ since both line segments are radii of the circle.
$AO \cong AO$ by identity since they are the same line segment.
Note that $\angle AFO \cong \angle AEO = 90^{\circ}$, since the line segments $AB$ and $AC$ are tangent to the circle.
Then, using the Pythagorean Theorem, we can show that $AF \cong AE$:
$\overline{AF} = \sqrt{(AO)^2-(OF)^2} = \sqrt{(AO)^2-(OE)^2} = \overline{AE}$
Since all three sides are congruent, $~~\triangle AOF \cong \triangle AOE~~$ by SSS
