9 units
1) If the Circumference is 36 then we can find the radius.
[tex]\begin{gathered} C=2\pi R \\ 36=2\pi R \\ \frac{36}{2\pi}=\frac{2\pi\cdot R}{{2\pi}}\frac{}{} \\ R=\frac{18}{\pi} \end{gathered}[/tex]
2) Now we can find the length of that arc AC, using this formula and plugging the radius:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi\cdot r \\ l=\frac{90}{360}\cdot2\pi\cdot\frac{18}{\pi} \\ l=\frac{1}{4}\cdot36 \\ l=9 \end{gathered}[/tex]
3) Hence, the length of that arc AC is 9 units
