Central Angle Of A Circle Formula With Solved Examples - Byju's

The angle between two radii of a circle is known as the central angle of the circle. The two points of the circle, where the radii intersect in the circle (Note – The other end of the radii meets at the centre of the circle), forms a segment of the Circle called the Arc Length.

Formula to Find the Central Angle of a Circle –  \[ Central\;Angle\;\theta =\frac{Arc\;Length\times 360^{o}}{2\pi r}\]

Solved Examples

Example 1: Find the central angle, where the arc length measurement is about 20 cm and the length of the radius measures 10 cm.

Solution:

Given,

r = 10 cm

Arc length = 20 cm

The formula of central angle is,

Central Angle \(\begin{array}{l}\theta\end{array} \) = \(\begin{array}{l}\frac{Arc Length \times 360^{o}}{2 \times\pi \times r}\end{array} \)

Central Angle \(\begin{array}{l}\theta\end{array} \) = \(\begin{array}{l}\frac{20 \times 360^{o}}{2 \times 3.14 \times 10}\end{array} \)

Central Angle \(\begin{array}{l}\theta\end{array} \) = \(\begin{array}{l}\frac{7200}{62.8}\end{array} \) = 114.64°

Example 2: If the central angle of a circle is 82.4° and the arc length formed is 23 cm then find out the radius of the circle.

Solution:

Given, 

Arc length = 23 cm

The formula of central angle is,

Central Angle \(\begin{array}{l}\theta\end{array} \) = \(\begin{array}{l}\frac{Arc\;Length \times 360^{o}}{2\times\pi \times r}\end{array} \)

82.4° = \(\begin{array}{l}\frac{23 \times 360^{o}}{2\times\pi \times r}\end{array} \)

82.4° = \(\begin{array}{l}\frac{8280}{6.28\times r}\end{array} \)

r= \(\begin{array}{l}\frac{8280}{6.28\times 82.4}\end{array} \)

r = 16 cm

Comments

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

* Send OTP Did not receive OTP?

Request OTP on Voice Call

* * Post My Comment

1. 

   Tashu December 2, 2019 at 10:15 pm

   Very nice answer and solution.

   Reply

Register with BYJU'S & Download Free PDFs

* Send OTP * * * * * Grade Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12 IAS CAT Bank Exam GATE Download Now

Register with BYJU'S & Watch Live Videos

* Send OTP * * * * * Grade Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12 IAS CAT Bank Exam GATE Watch Now