Question

If in two circles, arcs of same length subtend angles 60° and 75º at the center, find the ratio of their radii?
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Answer 1

Answer:

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θ

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θTherefore,

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θTherefore,l = r1 × π/3 and l = r2 × 5π/12

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θTherefore,l = r1 × π/3 and l = r2 × 5π/12⇒ r1 × π/3 = r2 × 5π/12

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θTherefore,l = r1 × π/3 and l = r2 × 5π/12⇒ r1 × π/3 = r2 × 5π/12On solving them taking r on one side, we get

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θTherefore,l = r1 × π/3 and l = r2 × 5π/12⇒ r1 × π/3 = r2 × 5π/12On solving them taking r on one side, we get⇒ r1 / r2 = 5π/12 × 3/π

Let the arc of length l1 subtend angles 60° at the centre and the arc of the length l2 be 75° at the centre.⇒ 60° = π/3 radian and 75° = 5π/12 radian using θ = l / r.As we know that in a circle or radius r, the arc length l subtend at an angle θ radian at the centre, then θ = l / r or l = r θTherefore,l = r1 × π/3 and l = r2 × 5π/12⇒ r1 × π/3 = r2 × 5π/12On solving them taking r on one side, we get⇒ r1 / r2 = 5π/12 × 3/π ⇒ r1 / r2 = 5/4