The angle subtended by an arc of length 20 cm at the centre of circle when radius is 14 cm is

Options

A. `5/(7)` radians
B. `10/(7)` radians
C. `5/(14)` radians
D. `7/(10)` radians

Answer

To find the angle subtended by an arc at the center of a circle, we can use the formula:

\[ \theta = \frac{L}{r} \]

where:
- \( \theta \) is the angle in radians,
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle.

Given:
- Length of the arc \( L = 20 \) cm,
- Radius of the circle \( r = 14 \) cm.

Now, we can substitute the values into the formula:

\[ \theta = \frac{L}{r} = \frac{20 \text{ cm}}{14 \text{ cm}} \]

Next, we simplify the fraction:

\[ \theta = \frac{20}{14} = \frac{10}{7} \text{ radians} \]

Thus, the angle subtended by the arc at the center of the circle is:

\[ \theta = \frac{10}{7} \text{ radians} \]

**Final Answer: \( \frac{10}{7} \) radians**

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