The angle subtended at the center of a circle by an arc can be found using the formula:

$\theta = \frac{L}{r}$

Where:

• $\theta$ is the angle in radians,
• $L$ is the length of the arc, and
• $r$ is the radius of the circle.

Given:

• Arc length ($L$) = 11 cm,
• Radius ($r$) = 21 cm,

Substitute the values into the formula:

$\theta = \frac{11}{21}$

$\theta = 0.5238 \text{ radians}$

Thus, the angle subtended at the center of the circle by the arc is approximately 0.5238 radians.

Would you like to convert this to degrees or need further details?

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Here are 5 questions related to the concept:

1. How do you convert an angle from radians to degrees?
2. What is the formula for finding the length of an arc given the angle and radius?
3. How do we find the area of a sector of a circle using the angle?
4. What happens to the subtended angle if the radius is doubled while keeping the arc length constant?
5. How can we find the angle subtended at the center if the perimeter of the sector is given?

Tip: To convert an angle from radians to degrees, use the conversion: $1 \text{ radian} = \frac{180}{\pi} \text{ degrees}$.