How to find the minor arc of a circle?

Understand the Problem

The question is asking how to determine the length of the minor arc of a circle. This involves understanding the geometry of circles, specifically the definition of an arc and how to calculate its length based on the circle's radius and the angle subtended by the arc at the center of the circle.

Answer

The length of the minor arc is given by $L = r \theta$, where $\theta$ is in radians.

Steps to Solve

Identify the parameters
Determine the radius of the circle and the angle in degrees or radians that subtends the arc. Let's denote the radius as $r$ and the angle as $\theta$.
Convert the angle if necessary
If the angle is in degrees, convert it to radians as the formula for arc length requires the angle to be in radians. The conversion can be done using the formula:
$$ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} $$
Or, if the angle is already in radians, proceed to the next step.
Apply the arc length formula
The length of the minor arc $L$ can be calculated using the formula:
$$ L = r \theta $$
where $r$ is the radius, and $\theta$ is the angle in radians.
Calculate the arc length
Substitute the values of $r$ and $\theta$ into the arc length formula and perform the calculation to find $L$.

The length of the minor arc $L$ is calculated as $L = r \theta$ where $r$ is the radius and $\theta$ is the angle in radians.

More Information

The length of an arc is a important concept in geometry as it helps in understanding the proportion of a circle that the arc represents. The minor arc is the shorter of the two arcs created by dividing a circle with a chord.

Tips

Mixing up degrees and radians: Always ensure you convert degrees to radians for the arc length formula.
Not using the correct formula for minor arcs: Remember that the formula specifically represents the length of the arc based on the central angle.

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