The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.

9 cm

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7 cm

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2 cm

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6 cm

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Solution

The correct option is D
6 cm

Given: OP = 10 cm and radius OT = 8 cm

$∵ O T ⊥ P T$ [By Theorem- The tangent at any point of a circle is perpendicular to the radius through the point of contact.]

$∴$ Applying pythagoras theorem in right $Δ O T P$ ,

$O P^{2} = O T^{2} + P T^{2} \Rightarrow (10)^{2} = (8)^{2} + P T^{2}$

$\Rightarrow 100 = 64 + P T^{2} \Rightarrow P T^{2} = 100 - 64 = 36$

$∴ P T = \sqrt{36} = 6 c m$

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