# If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

**Solution:**

Let the radii of the circles be r_{1} and r_{2} be the radii of the two circles.

Let the arc of length l_{1} subtend angles 60° at the centre and the arc of the length l_{2} 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

Therefore,

l = r_{1 }× π/3 and l = r_{2 }× 5π/12

⇒ r_{1 }× π/3 = r_{2 }× 5π/12

On solving them taking r on one side, we get

⇒ r_{1 }/ r_{2 }= 5π/12 × 3/π

⇒ r_{1 }/ r_{2 }= 5/4

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.1 Question 6

## If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

**Summary:**

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, then the ratio of the radii of the two circles is 5 : 4

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