Elementary Geometry for College Students (6th Edition)

Since all three sides are congruent, $~~\triangle AOF \cong \triangle AOE~~$ by SSS
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