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in Trigonometric Functions by (46.3k points)

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

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Let radii of circle r1 and r2.

then angle substened by an arc at the centre of first circle is

θ = 60° = π /3 radian

Angle subtended by an arc at the centre of second circle is

= 75° = 75π /180 = 5π /12

From formula : Length of arc ( l )

= radius (r) x angle (θ)

∴ Length of arc of first circle = π /3 x r1

Length of arc of second circle = 5π /12 x r2

Given that: Arcs of two circles are of same length

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