A chord of a circle subtends an angle of 60° at the circumference of the circle. What is the ratio of the radius of the circle to the length of the chord respectively?
वृत्त की एक जीवा वृत्त की परिधि पर 60° का कोण बनाती है। वृत्त की त्रिज्या और जीवा की लंबाई का अनुपात ज्ञात कीजिए।
This Question Asked In:
SSC, CGL MAINS 2026
Correct Answer :A - 1 : 1
Detailed Text Solution
If a chord subtends an angle of 60° at the circumference, then it subtends 120° at the center.
Let radius = R.
Length of chord = 2R sin(θ/2), where θ is central angle.
Here θ = 120°.
Chord length = 2R sin(120°/2)
= 2R sin(60°)
= 2R × (√3/2)
= R√3.
Thus ratio of radius to chord length = R : R√3
= 1 : √3.