Answer: The radius of the circle is 19.1 inches.
The length l of an arc corresponding to a central angle x (in radians) is:
[tex]l = x\cdot r[/tex]
Given the values for l and x:
[tex]45 = \frac{3}{4}\pi\cdot r\\\implies r = \frac{4}{3\pi}45=\frac{60}{\pi}\approx\frac{60}{3.14}\approx 19.1[/tex]
The above is in inches.
