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GRE
GRE Quantitative Reasoning Section

Arc Length of Circular Segment

Very Hard Geometry Circles

In a circular park with a radius of 12 meters, a path is built along the circumference for walking. A segment of this path creates a central angle of 120 degrees from the center of the circle. Calculate the length of the path along the segment of the circular park.

Use the formula for the arc length, which is given by:

$$ L = r \theta $$

where $L$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians. Note that to convert degrees to radians, you can use the conversion factor:

$$ \text{radians} = \text{degrees} \times \f\frac{\pi}{180} $$

Hint

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