Question

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.

Class X1 - Maths -Trigonometric Functions Page 55

Answer 1

Let L is the arc length of both circles. r1 and r2 are the radius of given circles respectively.

Use the formula,
∅ = L/R

For circle , arc subtended angle of 60° at the centre .
∅1 = 60° = 60×π/180 = π/3 rad
r1 = L/(π/3) = 3L/π ------(1)

For circle, arc subtended angle of 75° at the centre.
∅2 = 75° = 75×π/180° = 5π/12
So, r2 = L/∅2
= L/(5π/12)
= 12L/5π -------(1)

Divide eqns (1)÷ (2)

r1/r2 = (3L/π)/(12L/5π)
= 5/4
Hence, ratio of their radius = 5:4