Question

8.
If the length of a chord of a circle at a distance of 24 cm from the centre of the circle is 36 cm,
find the length of the greatest chord of the circle.
(a) 80 cm (b) 70 cm (c) 60 cm (d) 50 cm​

Answer 1

Answer:

H

2

=B

2

+P

2

Then given that

Distance between chord from radius =5 cm

Length of chord =24 cm

H

2

=B

2

+P

2

H=

(12)

2

+(5)

2

⇒H=

144+25

⇒H=

169

⇒H=

(13)

2

⇒H=13cm

∴ Radius of the circle =13 cm.

Diameter of the circle =2×radius=2×13=26cm.

Answer 2

Given,

Length of a chord of a circle = 36 cm

Distance of the chord from the center of the circle = 24 cm

To find,

The length of the greatest chord of the circle.

Solution,

We can simply solve this mathematical problem using the following process:

As per geometry;

In any circle, the line segment joining the center of the circle with the midpoint of the chord determines the distance of the chord from the center of the circle. This line segment is perpendicular to the chord at the midpoint. This line segment, half of the chord and the respective radius of the circle, joining the center and one end of the chord, forms a right-angled triangle.

Also, the greatest chord of a circle is its diameter.

Now, according to the question;

applying Pythagoras theorem to the right-angled triangle formed by the distance of the given chord, half of the chord, and their respective radius, we get;

(radius)^2 = (distance of the chord)^2 + (length of the chord/2)^2

=> (radius)^2 = (24)^2 + (36/2)^2 = (24)^2 + (18)^2

=> (radius)^2 = 6^2 {(4)^2 + (3)^2} = (6)^2 x (5)^2

=> radius = (6 x 5) cm

=> radius = 30 cm

Now,

The length of the greatest chord of the circle

= length of the diameter of the circle

= 2 x radius of the circle

= 2 x 30 cm

= 60 cm

Hence, the length of the greatest chord of the circle is equal to 60 centimeters. (Option-C)