A circle has a center at #(3 ,1 )# and passes through #(2 ,1 )#. What is the length of an arc covering #pi/8# radians on the circle?

From the given data: A circle has a center at (3,1) and passes through (2,1). What is the length of an arc covering π/8 radians on the circle?

We need the radius r to compute for the arc

God bless...I hope the explanation is useful.

To find the length of an arc covering $\frac{\pi}{8}$ radians on a circle, you can use the formula:

$\text{Arc Length} = r \times \theta$

where $r$ is the radius of the circle and $\theta$ is the angle in radians.

Given that the circle has a center at $(3, 1)$ and passes through $(2, 1)$, we can find the radius $r$ using the distance formula:

$r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$r = \sqrt{(2 - 3)^2 + (1 - 1)^2}$

$r = \sqrt{1 + 0}$

$r = 1$

Now, plug in the values of $r = 1$ and $\theta = \frac{\pi}{8}$ into the arc length formula:

$\text{Arc Length} = 1 \times \frac{\pi}{8}$

$\text{Arc Length} = \frac{\pi}{8}$