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Question -

Find the length of a tangent drawn to a circle with radius 5 cm, from a point 13 cm from the centre of the circle.



Answer -

From a point P outside the circle with centre O, PT is the tangent to the circle and radius
OT = 5 cm, OP = 15 cm
 
OT ⊥ PT
Now in right ∆OPT,
OP² = OT² + PT² (Pythagoras Theorem)
(13)² = (5)² + PT²
=> 169 = 25 + PT²
=> PT² = 169 – 25 = 144 = (12)²
PT = 12 cm

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