Answer: [tex]27\pi[/tex]
Step-by-step explanation:
In the given figure we have given a circle in with radius PC = 18 inches
Also, the central angle made by arc AC [tex]90^{\circ}[/tex] or [tex]\dfrac{\pi}{2}[/tex]
Since the sum of angles at a point is [tex]2\pi[/tex]
Then , the central angle made by arc AC :-
[tex]\theta=2\pi-\dfrac{\pi}{2}=\dfrac{3\pi}{2}[/tex]
The formula to find the arc length is given by :-
[tex]l=r\theta[/tex]
Then the length of arc ABC will be :-
[tex]l=(18)(\dfrac{3\pi}{2})=27\pi[/tex]
Hence, the length of arc ABC = [tex]27\pi[/tex]
