Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is :
(a) \( 2 \) units
(b) \( \pi \) units
(c) \( 4 \) units
(d) \( 7 \) units


Answer :


Here, \( 2 \pi r \ = \ \pi r^2 \), where r is the radius

\( \Rightarrow \ r^2 \ - \ 2r \ = \ 0 \)

\( \Rightarrow \ r(r \ - \ 2) \ = \ 0 \)

\(\Rightarrow \ r \ = \ 0 \ or \ r \ = \ 2 \)

But, \( r \ \ne \ 0 \) \(\therefore \) \(r \ = \ 2 \) units

Hence the correct option is (a).

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