Answer:
The length of arc OP is 1/8 the circumference of the circle
Step-by-step explanation:
step 1
Find the circumference of the circle L
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=5\ units[/tex]
substitute
[tex]C=2\pi (5)[/tex]
[tex]C=10\pi\ units[/tex]
step 2
Find the length of arc OP
we know that the circumference of the circle subtends a central angle of 360 degrees
so
using proportion
Find out the length of the arc OP by a central angle of 45 degrees
Let
x -----> the length of arc OP
[tex]\frac{10\pi}{360}=\frac{x}{45}\\\\x=10\pi(45)/360\\\\x=10\pi(\frac{1}{8})\ units[/tex]
therefore
The length of arc OP is 1/8 the circumference of the circle
