Question

The radius of a circle is decreased by 2m, then the ratio of the area of the original circle to the reduced circle becomes 3 : 1. Find its radius.

(A) (√3+1) m

(C) (13-1) m
(B) (√3+3) m

(D) 2√3 m​

Answer 1

Given info : The radius of a circle is decreased by 2m, then the ratio of the area of the original circle to the reduced circle becomes 3 : 1.

To find : the radius of the circle is ...

solution : let the radius of the circle is r.

initial area of circle , A = πr²

now radius is decreased by 2m, i.e., (r - 2)

so, area, A' = π(r - 2)²

a/c to question, A/A' = 3/1

⇒πr²/π(r - 2)² = 3/1

⇒r/(r - 2) = √3/1

⇒r = √3r - 2√3

⇒(√3 - 1)r = 2√3

⇒r = 2√3/(√3 - 1) = 2√3(√3 + 1)/2 = √3(√3 + 1)

= 3 + √3

Therefore the radius of the circle is 3 + √3.

Answer 2

Answer:

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