Question

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central angle bac of circle a measures \\(\frac{23}{20}\pi\\) radians. arc bc has a length of 63.48\\(\pi\\) centimeters. what is the radius of the circle?
the radius of circle a is
207
110.4
993.6
55.2
centimeters.
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Explanation:

Step1: Recall arc length formula

The formula for arc length $s$ with central angle $\theta$ (in radians) is $s = r\theta$, where $r$ is the radius.

Step2: Substitute given values

We know $s = 63.48\pi$ and $\theta = \frac{22}{20}\pi$. Substitute into the formula:
$$63.48\pi = r \times \frac{22}{20}\pi$$

Step3: Solve for $r$

Cancel $\pi$ from both sides, then rearrange to isolate $r$:
$$r = 63.48 \times \frac{20}{22}$$
Calculate the value:
$$r = 63.48 \times \frac{10}{11} = 55.2$$

Answer:

55.2