# HOW TO CALCULATE LENGTH OF CHORD IN CIRCLE

## About "How to calculate length of chord in circle"

How to calculate length of chord in circle :

Here we are going to see how to find length of chord in a circle.

To find the length of chord, we may use the following theorem

• Perpendicular from the centre of a circle to a chord bisects the chord.

Example 1 :

A chord is 8 cm away from the centre of a circle of radius 17 cm. Find the length of the chord.

Solution :

Distance of chord from center of the circle  =  8 cm

Radius of the circle  =  17 cm

Length of chord  =  AB

Here the line OC is perpendicular to AB, which divides the chord of equal lengths.

In Δ OCB,

OB2  =  OC2 + BC2

172  =  82 + BC2

BC2  =  172 - 82

BC  =  √(172 - 82)

BC  =  √289 - 64

BC  =  √225

BC  =  √(15 ⋅ 15)

BC  =  15 cm

Length of chord  =  AB  =  2 (Length of BC)

=  2 (15)

=  30 cm

Hence the length of chord is 30 cm.

Example 2 :

Find the length of a chord which is at a distance of 15 cm from the centre of a circle of radius 25 cm.

Solution :

Distance of chord from center of the circle  =  15 cm

Radius of the circle  =  25 cm

Length of chord  =  AB

Here the line OC is perpendicular to AB, which divides the chord of equal lengths.

In Δ OCB,

OB2  =  OC2 + BC2

252  =  152 + BC2

BC2  =  252 - 152

BC  =  √(252 - 152)

BC  =  √625 - 225

BC  =  √400

BC  =  √(20 ⋅ 20)

BC  =  20 cm

Length of chord  =  AB  =  2 (Length of BC)

=  2 (20)

=  40 cm

Hence the length of chord is 40 cm.

Example 3 :

A chord of length 20 cm is drawn at a distance of 24 cm from the centre of a circle. Find the radius of the circle.

Solution :

Here the line OC is perpendicular to AB, which divides the chord of equal lengths.

In Δ OCB,

OB2  =  OC2 + BC2

OB2  =  242 + 102

BC2  =  576 + 100

BC2  =  676

BC  =  √676

BC  =  √(26 ⋅ 26)

BC  =  26  cm

Hence the radius of the circle is 26 cm.

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