Answer
384.3k+ views
Hint: Here, we have to find the distance of the chord from the centre. We will find the chord length using Perpendicular distance from the centre. The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle.
Formula Used:
Chord length Using Perpendicular distance from the centre is given by \[{\text{Chord Length}} = 2 \times \sqrt {\left( {{r^2} - {d^2}} \right)} \], where \[d\] is the perpendicular distance of the chord from the centre and \[r\] is the radius of the circle.
Complete Step by Step Solution:
We will draw a circle with radius of a circle \[r\] as 13 cm and chord of a circle \[l\] as 10 cm.
Let AC be the chord of a circle, OP be the radius of the circle and OB be the distance between the chord of a circle and radius of a circle.
Length of the chord \[ = 10{\text{cm}}\]
\[ \Rightarrow l = \dfrac{{10}}{2}\]
Dividing the terms, we get
\[ \Rightarrow l = {\text{5 cm}}\]
By using the formula \[{\text{Chord Length}} = 2 \times \sqrt {\left( {{r^2} - {d^2}} \right)} \], we have
\[d = \sqrt {{r^2} - {{\left( {\dfrac{l}{2}} \right)}^2}} \]
Substituting the values \[r = {\text{13 cm}}\] and \[\dfrac{l}{2} = {\text{5 cm}}\]
\[ \Rightarrow d = \sqrt {{{13}^2} - {5^2}} \]
The square of the number 13 is 169.
The square of the number 5 is 25.
Squaring the terms, we get
\[ \Rightarrow d = \sqrt {169 - 25} \]
\[ \Rightarrow d = \sqrt {144} \]
Computing the square root, we get
\[ \Rightarrow d = {\text{12 cm}}\]
Therefore, the distance of the chord from the centre is 12cm.
Note:
We know that in a circle, perpendicular from the centre bisects the chord. Among the properties of the chord of a circle, Chords are equidistant from the center if and only if their lengths are equal. A chord that passes through the center of a circle is called a diameter and is the longest chord. A radius or diameter that is perpendicular to a chord divides the chord into two equal parts. It means that both the halves of the chords are equal in length. The perpendicular bisector of a chord passes through the center of a circle. The formula can also be used to find the length of the cord and the radius of the circle by rewriting the equation.
Formula Used:
Chord length Using Perpendicular distance from the centre is given by \[{\text{Chord Length}} = 2 \times \sqrt {\left( {{r^2} - {d^2}} \right)} \], where \[d\] is the perpendicular distance of the chord from the centre and \[r\] is the radius of the circle.
Complete Step by Step Solution:
We will draw a circle with radius of a circle \[r\] as 13 cm and chord of a circle \[l\] as 10 cm.
![seo images](https://www.vedantu.com/question-sets/c07776fd-7149-44a1-97e8-80737cdf76613460103137779485095.png)
Let AC be the chord of a circle, OP be the radius of the circle and OB be the distance between the chord of a circle and radius of a circle.
Length of the chord \[ = 10{\text{cm}}\]
\[ \Rightarrow l = \dfrac{{10}}{2}\]
Dividing the terms, we get
\[ \Rightarrow l = {\text{5 cm}}\]
By using the formula \[{\text{Chord Length}} = 2 \times \sqrt {\left( {{r^2} - {d^2}} \right)} \], we have
\[d = \sqrt {{r^2} - {{\left( {\dfrac{l}{2}} \right)}^2}} \]
Substituting the values \[r = {\text{13 cm}}\] and \[\dfrac{l}{2} = {\text{5 cm}}\]
\[ \Rightarrow d = \sqrt {{{13}^2} - {5^2}} \]
The square of the number 13 is 169.
The square of the number 5 is 25.
Squaring the terms, we get
\[ \Rightarrow d = \sqrt {169 - 25} \]
\[ \Rightarrow d = \sqrt {144} \]
Computing the square root, we get
\[ \Rightarrow d = {\text{12 cm}}\]
Therefore, the distance of the chord from the centre is 12cm.
Note:
We know that in a circle, perpendicular from the centre bisects the chord. Among the properties of the chord of a circle, Chords are equidistant from the center if and only if their lengths are equal. A chord that passes through the center of a circle is called a diameter and is the longest chord. A radius or diameter that is perpendicular to a chord divides the chord into two equal parts. It means that both the halves of the chords are equal in length. The perpendicular bisector of a chord passes through the center of a circle. The formula can also be used to find the length of the cord and the radius of the circle by rewriting the equation.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)