Will it be true to say that the perimeter of a square circumscribing a circle of radius 'a' cm is '8a' cm?

Yes, since side of the square is 2a cm

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No, since side of the square is a cm

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Yes, since side of the square is 8a cm

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No, since side of the square is 8a cm

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Solution

The correct option is A Yes, since side of the square is 2a cm
$G i v e n - O i s t h e c e n t r e o f a c i r c l e w i t h c e n t r e O a n d r a d i u s a i n s c r i b e d i n t h e s q u a r e P Q R S . T o f i n d o u t = w h e t h e r t h e p e r i m e t e r o f P Q R S i s 8 a o r n o t . S o l u t i o n - W e j o i n B D & A C . S i n c e t h e y a r e d i a m e t e r e s o f t h e g i v e n c i r c l e, t h e y w i l l i n t e r s e c t a t t h e c e n t r e O . N o w Q R i s a t a n g e n t t o t h e c i r c l e s i n c e t h e c i r c l e i s i n s c r i b e d i n t h e s q u a r e P Q R S . ∴ ∠ O B Q = 90^{o} . A n d ∠ B Q C = 90^{o} s i n c e i t i s t h e a n g l e o f a s q u a r e . A l s o O B = O C (r a d i i o f t h e s a m e c i r l e) . ∴ O B Q C i s a s q u a r e . ∴ O C = a = Q B . S i m i l a r l y, c o n s i d e r i n g O B R A, w e h a v e B R = O A = a . ∴ Q B + B R = Q R = a + a = 2 a . ∴ T h e p e r i m e t e r o f P Q R S = 4 \times 2 a = 8 a . S o t h e g i v e n s t a t e m e n t i s c o r r e c t s i n c e t h e s i d e o f P Q R S = 8 a . A n s - O p t i o n A$

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Similar questions

If the side of a square is 8a cm, what is its area?

x = (1 + sin A) (1 + sin B) (1 + sin C) = (1 - sin A) (1 - sin B) (1 - sin C),

\pm cos A cos B cos C .

a

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