If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is

3 cm

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6 cm

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9 cm

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1 cm

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Solution

The correct option is C 6 cm
$G i v e n - T h e r a d i i o f t w o c o n c e n t r i c c i r l e s w i t h c e n t r e O a r e 5 c m & 4 c m . T h e c h o r d A B o f o u t e r c i r c l e t o u c h e s t h e i n n e r c i r c l e a t P . T o f i n d o u t - T h e l e n g t h o f A B = ? .$
The radius of a circle is at the right angle at the point of contact of the tangent to the circle with the tangent.
$S o l u t i o n - A B t o u c h e s t h e i n n e r c i r c l e a t P . ∴ A B = 2 A P, O P ⊥ A B ⟹ Δ A O P i s a r i g h t a n g l e d o n e w i t h A O a s t h e h y p o t e n u s e . N o w i n Δ A O P A O = 5 C M, O P = 4 c m ∴ A P = \sqrt{{A O}^{2} - {A P}^{2}} = \sqrt{5^{2} - 4^{2}} c m = 3 c m . ∴ A B = 2 A P = 2 \times 3 c m = 6 c m A n s - O p t i o n B$

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Q. In two concentric circles, the radii are

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is the tangent to the circle of radius

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cm, then find the length of the chord of the bigger circle.

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