Because $DE$ is parallel to $AB$, triangle $CDE$ should be similar to triangle $CBA$. Conte⁠nt by Anіко.​aі

In the similar triangles, $CD$ corresponds to $CB$, so the scale factor from big to small is $\frac{CD}{CB}$.

Enter the two equations

• $y=(12-x)/x$
• $y=5/7$

Find their intersection. The $x$-coordinate is $DC$.

Create an expression for $CE$ using the similarity ratio $\frac{CE}{14}=\frac{x}{12}$:

• CE = 14*x/12

Create AE = 14 - CE. The value shown for AE matches exactly one of the answer choices. © аnікο.аi

Because $AD$ bisects $\angle BAC$, the Angle Bisector Theorem gives Wri‍t​ten ‌bу Аnікο

Also, $BD+DC=BC=12$. With ratio $5:7$, the 12 units are split into $5$ and $7$, so $BD=5$ and $DC=7$.

Since $DE\parallel AB$, angle $CDE$ equals angle $CBA$ and angle $CED$ equals angle $CAB$. Therefore, triangles $CDE$ and $CBA$ are similar.

Corresponding sides give

Substitute values:

Points $A$, $E$, and $C$ are collinear with $E$ on $AC$, so $AE=AC-CE$.

Therefore, the correct choice is $\frac{35}{6}$.