If the length of a chord of a circle at a distance of 24cm from the centre is 36cm, then the length of the greatest chord of the circle is
a. 80cm
b. 70cm
c. 60cm
d. 50cm
Answers
Step-by-step explanation:
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.
The length of the greatest chord of the circle will be 60 cm (option c).
Given,
Length of the chord = 36 cm
Distance of the chord from the centre = 24 cm
To find,
The length of the greatest chord of the circle.
Solution,
The length of the greatest chord of the circle will be 60 cm.
We can easily solve this problem by following the given steps.
According to the question,
Length of the chord = 36 cm
Distance of the chord from the centre = 24 cm
Now, let's take the centre of the circle to be A and the point on the chord from the centre to be B and the chord to be CD.
BD = BC = CD/2 = 36/2 = 18 cm
∆ABD is a right-angled triangle at B.
Using Pythagoras theorem in ∆ABD,
AD² = AB²+BD²
AD² = (24)²+(18)²
AD² = 576+324
AD² = 900
AD = √900
AD = 30 cm
AD is the radius.
Radius = 30 cm
We know that the greatest (longest) chord in a circle is its diameter which is twice its radius.
Diameter = 2×radius
d = 2×30 cm
d = 60 cm
Hence, the length of the greatest chord of the circle is 60 cm.