Arc

Arc Length Formula

The smooth curve that joins two endpoints, is known as the arc. In Mathematics, the arc is the part of a circle. Besides that, the arc can also be a part of other shapes - like the sphere, the ellipse, cylinder, etc. In this article, we will be studying the basics of the arc, arc meaning, the measures of the arc, arc of the circle definition, what is an arc in Math, the arc length formula, and the derivation of the length formula. 


Arc of a Circle

The part of a circle or a specific segment of the circumference of the circle is known as the arc of the circle. When you try and connect the two ends of the arc, a line is formed. This line is known as the chord of the circle.  If the arc’s length is exactly equal to the half of the circle, then it is called a semicircular arc. 

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You name the arc depending on the variables at its endpoints. In the above figure, you can notice the arc. It is named as PQ. It can be called as PQ or as arc PQ. You can also represent it with the help of a curved line and can be denoted asPQ^

FAQ (Frequently Asked Questions)

1) What is the Arc in Math? How do you Denote it?

The part of a circle or a specific segment of the circumference of the circle is known as the arc of the circle. When you try and connect the two ends of the arc, a line is formed. This line is known as the chord of the circle.  If the arc’s length is exactly equal to the half of the circle, then it is called a semicircular arc. You name the arc depending on the variables at its endpoints. In the above figure, you can notice the arc. It is named as PQ. It can be called as PQ or as arc PQ. You can also represent it with the help of a curved line and can be denoted as (PQ)^ and it can be read as arc PQ.

2) What is the arc length formula in measure and radians?

The angle measure is nothing but the angle that is created with the help of the arc at the middle at the circle. To denote the same, the arc is preceded with the help of a lowercase letter M ( indicating Measure ). For example, m

(PQ)= 90˚ cm is read as “ the measure of the arc PQ is equal to 90˚ degrees.”

When you measure the arc length in degree, the formula is given by: 


s = 2 *𝛑* r ( Ө/360 )


When you measure the arc length in radians, the formula is given by: 


s = r * Ө

Where,

s - is the arc length

Ө - denotes the central angle of the arc in measure/radians

r - is the radius of the arc