A point $P$ is $17 c m$ away from the centre of the circle and the length of tangent drawn from $P$ to the circle is $15 c m$ . Find the radius of the circle.

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Solution

$G i v e n - O i s t h e c e n t r e o f a c i r c l e t o w h i c h a t a n g e n t P Q h a s b e e n d r a w n t o t h e c i r c l e a t Q w h e n O P = 17 c m . P Q = 15 c m T o f i n d o u t - T h e r a d i u s o f t h e g i v e n c i r c l e = ? S o l u t i o n - W e j o i n O Q . ∴ O Q i s a r a d i u s o f t h e c i r c l e t h r o u g h t h e p o i n t o f c o n t a c t T o f t h e t a n g e n t P Q . W e k n o w t h a t t h e r a d i i t h r o u g h t h e p o i n t o f c o n t a c t o f a t a n g e n t t o a c i r c l e i s p e r p e n d i c u l a r t o t h e t a n g e n t . ∴ O Q ⊥ P Q ⟹ ∠ O Q P = 90^{o} . ∴ Δ O Q P i s a r i g h t o n e w i t h O P a s h y p o t e n u s e . S o, a p p l y i n g P y t h a g o r a s t h e o r e m, w e g e t O Q = \sqrt{{O P}^{2} - {P Q}^{2}} = \sqrt{17^{2} - 15^{2}} c m = 8 c m . T h e r a d i u s o f t h e g i v e n c i r c l e = 8 c m ∴ A n s - O p t i o n - C$

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