Homeclass 10MathsAreas Related to CirclesCircular Arc

Circular Arc

A circular arc is a continuous portion of the circumference of a circle. It is defined by two endpoints on the circle and the curved line connecting them, representing a fraction of the circle's total boundary.

Key Concepts

An arc is classified into two types based on its length relative to a semicircle: a minor arc (shorter than a semicircle) and a major arc (longer than a semicircle).
The length of a circular arc is directly proportional to the central angle it subtends at the center of the circle.
When calculating the perimeter of a sector, the length of the corresponding circular arc is added to the lengths of the two bounding radii.

Formula & Equation

l=θ360∘×2πrl = \frac{\theta}{360^\circ} \times 2\pi r

l = length of the circular arc, \theta = central angle subtended by the arc in degrees, r = radius of the circle, \pi = mathematical constant (approximately \frac{22}{7})

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Common Misconceptions

Myth: Students often confuse the length of an arc with the area of a sector.
Fact: The length of an arc only measures the one-dimensional curved boundary (a part of the circumference), whereas the area of a sector measures the two-dimensional space enclosed by the arc and two radii.

Real World Applications

The curved outer crust of a slice of pizza represents a circular arc, where the entire pizza is the full circle.
A rainbow forms a circular arc in the sky, representing a visible portion of a complete circle of refracted light.

Frequently Asked Questions

How do you find the length of a circular arc?
You can find the length of a circular arc by multiplying the ratio of its central angle to 360 degrees by the total circumference of the circle.
What is the difference between a minor arc and a major arc?
A minor arc subtends a central angle less than 180 degrees and is shorter than a semicircle, while a major arc subtends an angle greater than 180 degrees and is longer than a semicircle.

Keep Learning

Length of an ArcSector of a CircleCircumference