VerifiedHint: 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.
