Arc of a Circle

1. What is the circle’s arc?

The circumference of a circle’s arc, which lies between any two points on it, is measured in length. i.e., Any portion of a circle’s circumference is an arc. The arc’s angle is the angle generated by two line segments connecting a point to the endpoints of an arc at any given place.

2. What is the formula for the arc length of a circle?

A circle’s radius (r) and central angle (θ) are two variables used in the calculation for arc length. L stands for it, and the formula is

the equation L = rθ (π/180) if θ is given in degrees

if θ is in radians, then L = rθ is the formula.

3. How to Determine the Length of an Arc Using Radians?

The arc of a circle formula may be used to get the arc length when the central angle is specified in radians, which is given as L  = θ × r, when θ is in radians.

Where,

• L is the Arc Length,
• θ is the Center angle of the arc, and
• r is the circle radius.

4. What is the Angle in the Central?

The central angle is the angle that the arc at the center of the circle subtends.

5. What Angle is Inscribed?

An inscribed angle is the angle that the arc occupies at any point along the circle’s circumference.

6. How Can You Calculate an Arc’s Length Without the Radius?

The circle’s radius and center angle are unquestionably necessary in order to determine the arc’s length. However, if the radius is omitted, the sector area or chord length may have been provided instead. Apply the arc length formula after using the following calculations to find the radius.

• Sector area = (θ/360) × πr², if θ is in degrees (or) (1/2) r²θ
• Chord length = 2r sin (θ/2)

Arc of a Circle is a part of the circumference of a circle or we can also say the Arc of a Circle is some percentage of the circle’s circumference. As we know, a circle is defined as a two-dimensional geometrical object where all the points are equidistant from the center and the distance measured around the circle is known as a circumference and some portion of the circumference taken at a time is known as the Arc of a Circle.

In this article, we will learn the Arc of a Circle in detail, including its definition, types, and arc length formula. Other than that we will also discuss the angle subtended by an arc and the theorem related to this angle as well.