# 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

Sum

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

#### 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