The radius of circle is 12 inches
Solution:
Given that,
Consider circle c with angle [tex]\frac{3 \pi }{4} \text{ radians }[/tex]
Minor arc AB measures [tex]9 \pi[/tex] inches
Therefore, we can say,
[tex]Central\ angle\ in\ radians = \frac{3 \pi }{4}\\\\Arc\ length = 9 \pi[/tex]
To find: Radius of circle
The length of arc when angle given in radians is:
[tex]s = r \times \theta[/tex]
Where,
"s" is the arc length and "r" is the radius and [tex]\theta[/tex] is the central angle in radians
[tex]9 \pi = r \times \frac{3 \pi }{4}\\\\r = 9 \times \frac{4}{3}\\\\r = 12[/tex]
Thus the radius of circle is 12 inches
