Question

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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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Answer 1

Step-by-step explanation:

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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:-

then. π/3×r¹ = 5π/12×r²

r¹/r²=5×3/12=5/4

r¹:r²=5:4

Hence, the ratio of radius of circles are

r¹:r²=5:4

Hope It Helps Uh☺️.

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