Question

the angle substended by a chord of a circle to its centre is 60 degree,what is the ratio of length of chord to the radius

Answer 1

✬ Ratio = 1 : 1 ✬

Step-by-step explanation:

Given:

• The angle subtended by a chord of a circle to centre is 60°.

To Find:

• What is the ratio of length of chord to the radius ?

Solution: Let in given circle.

• OA = OB = Radius of circle.
• AB = Chord

[ Draw a perpendicular OC from O on AB such that it bisects the ∠AOB ]

• ∠AOC = 1/2(∠AOB) = 1/2(60) = 30°
• ∠BOC = 1/2(∠AOB) = 1/2(60) = 30°
• ∠OCA = ∠OCB = 90°

Now in ∆AOC , AC = CB

$\implies{\rm }$ sin AOC = AC/OA

$\implies{\rm }$ sin 30° = AC/OA

$\implies{\rm }$ 1/2 = AC/r

$\implies{\rm }$ r = 2AC

$\implies{\rm }$ r/2 = AC

Since, AC = CB so,

=> AB = AC + CB

=> AB = r/2 + r/2 = 2r/2

=> AB = r (Chord)

Hence, required ratio

=> Chord/Radius

=> r/r

=> 1 : 1

Answer 2

✬ Ratio = 1 : 1 ✬

Step-by-step explanation:

Given:

The angle subtended by a chord of a circle to centre is 60°.

To Find:

What is the ratio of length of chord to the radius ?

Solution: Let in given circle.

OA = OB = Radius of circle.

AB = Chord

[ Draw a perpendicular OC from O on AB such that it bisects the ∠AOB ]

∠AOC = 1/2(∠AOB) = 1/2(60) = 30°

∠BOC = 1/2(∠AOB) = 1/2(60) = 30°

∠OCA = ∠OCB = 90°

Now in ∆AOC , AC = CB

⟹ sin AOC = AC/OA

⟹ sin 30° = AC/OA

⟹ 1/2 = AC/r

⟹ r = 2AC

⟹ r/2 = AC

Since, AC = CB so,

=> AB = AC + CB

=> AB = r/2 + r/2 = 2r/2

=> AB = r (Chord)

Hence, required ratio

=> Chord/Radius

=> r/r

=> 1 : 1