Question : The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is:
Option 1: 5 cm
Option 2: 6 cm
Option 3: 7 cm
Option 4: 8 cm
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Correct Answer: 8 cm
Solution :
The length of the tangent drawn from an external point to a circle can be found using the Pythagorean theorem.
If the radius of the circle is $r$ and the distance from the centre of the circle to the external point is $d$, then the length of the tangent $t$ is,
$t = \sqrt{d^2 - r^2}$
Substituting the given values into the equation,
$t = \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} \text{ cm} = 8 \text{ cm}$
Hence, the correct answer is 8 cm.
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