Maharashtra State BoardHSC Science (General) 11th
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Answer the following : If two arcs of the same length in two circles subtend angles 65° and 110° at the centre. Find the ratio of their radii. - Mathematics and Statistics

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Sum

Answer the following :

If two arcs of the same length in two circles subtend angles 65° and 110° at the centre. Find the ratio of their radii.

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Solution

Let r1 and r2 be the radii of the two circles and let their arcs of same length S subtend angles of 65° and 110° at their centres.

Angle subtended at the centre of the first circle,

θ1 = 65°

= `(65 xx pi/180)^"c"`

= `((13pi)/36)^"c"`

∴ S = r1θ1 = `"r"_1((13pi)/36)`  ...(i)

Angle subtended at the centre of the second circle,

θ2 = 110°

= `(110 xx pi/180)^"c"`

= `((11pi)/18)^"c"`

∴ S = r2θ2 = `"r"_2((11pi)/18)`  ...(ii)

From (i) and (ii), we get

`"r"_1((13pi)/36) = "r"_2((11pi)/18)`

∴ `"r"_1/"r"_2 = 22/13`

∴ r1 : r2 = 22 : 13

Concept: Length of an Arc of a Circle
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 1 Angle and its Measurement
Miscellaneous Exercise 1 | Q 2. II (06) | Page 13
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