A point $A$ is $26 c m$ away from the centre of a circle and the length of tangent drawn from $A$ to the circle is $24 c m$ . Find the radius of the circle.

10 c m

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20 c m

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25 c m

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15 c m

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Solution

The correct option is A $10 c m$
$G i v e n - O i s t h e c e n t r e o f a c i r c l e t o w h i c h A T = 24 c m i s a t a n g e n t a t T . A O = 26 c m . T o f i n d o u t - T h e r a d i u s o f t h e g i v e n c i r c l e = ? S o l u t i o n - W e j o i n O T . T h e n O T i s a r a d i u s o f t h e g i v e n c i r c l e t h r o u g h T . ∴ O T ⊥ A T s i n c e t h e a n g l e b e t w e e n t h e t a n g e n t t o a c i r c l e a n d t h e r a d i u s t h r o u g h t h e p o i n t o f c o n t a c t = 90^{o} . S o Δ O A T i s a r i g h t o n e w i t h A O a s h y p o t e n u s e . ∴ A p p l y i n g P y t h a g o r a s t h e o r e m, w e h a v e O T = \sqrt{{A O}^{2} - {A T}^{2}} = \sqrt{26^{2} - 24^{2}} c m = 10 c m . S o t h e r a d i u s o f t h e c i r c l e i s 10 c m . A n s - O p t i o n - A .$

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A point A is 26cm away from the centre of a circle and the length of tangent drawn from A to the circle is 24cm. Find the radius of the circle.

A point $A$ is $26 c m$ away from the centre of a circle and the length of tangent drawn from $A$ to the circle is $24 c m$ . Find the radius of the circle.