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Q.

The length of the tangent drawn to a circle with radius 'r' from a point P
which is 'd' units away from the centre is

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a

$\sqrt{d^{2} + r^{2}}$

b

$\sqrt{d r}$

c

$\sqrt{d + r}$

d

$\sqrt{d^{2} - r^{2}}$

answer is A.

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Detailed Solution

Question Image

We know that $O Q ⊥ P Q$

In right angled $Δ O P Q$

$\begin{array}{l} {(O P)}^{2} = {(P Q)}^{2} + {(O Q)}^{2} \\ {(P Q)}^{2} = {(O P)}^{2} - {(O Q)}^{2} \\ P Q = \sqrt{d^{2} - r^{2}} \end{array}$

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The length of the tangent drawn to a circle with radius 'r' from a point P which is 'd' units away from the centre is