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Question

A point $$P$$ is $$25cm$$ from the centre of a circle. The radius of the circle is $$7cm$$ and length of the tangent drawn from $$P$$ to the circle is $$x$$ cm. The value of $$x=$$  is


A
20cm
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B
24cm
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C
18cm
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D
12cm
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Solution

The correct option is D $$24cm$$

Given- $$O$$ is the centre of a circle to which a tangent $$PT=x$$ has been drawn to the circle at $$T$$ when $$OP=25cm$$. The radius of the given circle$$=7cm$$
To find out: $$ x=?$$
Solution- We join $$OT$$.
$$\therefore OT$$ is a radius of the circle through the point of contact $$T$$ of the tangent $$PT$$. We know that the radius through the point of contact of a tangent to a circle is perpendicular to the tangent.  
$$\therefore  OT\bot PT\Longrightarrow \angle OTP={ 90 }^{ o }$$.
$$\therefore  \Delta OTP$$ is a right one with $$OP$$ as hypotenuse. So, applying Pythagoras theorem, we get
$$PT=\sqrt { { OP }^{ 2 }-{ OT }^{ 2 } } =\sqrt { { 25 }^{ 2 }-{ 7 }^{ 2 } } cm=24cm$$.
$$\therefore$$ The tangent to the given circle $$PT=24cm$$.
Ans- Option-B.


277517_238452_ans.png

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