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Question
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
Options
`sqrt(21)` cm
`3sqrt(21)` cm
`2sqrt(21)` cm
`4sqrt(21)` cm
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Solution
`2sqrt(21)` cm
Explanation:
The line from the centre to the tangent is perpendicular to the tangent.
∴ CS ⊥ ST
So, in right angled ΔCST, by the Pythagoras theorem,
CT2 = CS2 + ST2
(10)2 = (4)2 + ST2
ST2 = 100 – 16 = 84
⇒ ST = `2sqrt(21)`
Thus, the length of ST is `2sqrt(21)` cm.
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