The length of the tangent drawn from a point $8 c m$ away from the centre of a circle of radius $6 c m$ is $2 \sqrt{7} c m .$

True

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False

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Solution

The correct option is A: True

Given that $A O = 8 c m, B O = 6 c m$
Since $∠ A B O = 90^{\circ}$ [Tangent at the point of contact will be perpendicular to the radius]
Applying Pythagoras theorem in $△$ ABO,

${A B}^{2} = {A O}^{2} - {B O}^{2}$

$\Rightarrow {A B}^{2} = 8^{2} - 6^{2}$

$\Rightarrow {A B}^{2} = 64 - 36 = 28$

$\Rightarrow A B = 2 \sqrt{7} c m$

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