Answer
radius = 9
Step-by-step explanation
The relation between the central angle, θ (measured in radians), the arc length, and the radius, r, of a circle is shown in the next picture:
Substituting θ = 7π/6, and arc length = 21π/2, and solving for the radius:
[tex]\begin{gathered} \frac{21\pi}{2}=\frac{7\pi}{6}r \\ \frac{21\pi}{2}\cdot\frac{6}{7\pi}=\frac{7\pi}{6}r\cdot\frac{6}{7\pi} \\ 9=r \end{gathered}[/tex]
