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Byju's Answer

Standard XIII

Mathematics

Length of Tangent and Power of a Point

C is a circle...

Question

C is a circle centered at O. $P T_{1}$ and $P T_{2}$ are the tangents drawn from a point P outside the circle to the circle. Then which of these is the most appropriate relation.

$O P > P T_{2} = P T_{1}$

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$O P = P T_{1} = P T_{2}$

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$O P < P T_{1} \leq P T_{2}$

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$O P < P T_{1} = P T_{2}$

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Solution

The correct option is A
$O P > P T_{2} = P T_{1}$

Firstly, any 2 tangents drawn to a circle will have equal length

$i . e ., P T_{1} = P T_{2}$

Also, $△ O T_{1} P$ is right angled at $T_{1}$ and OP forms the hypotenuse, hence larger than other two sides $O T_{1}$ and $P T_{1}$ .

$∴$ Line joining centre and P is always greater than the lengths of the tangents.

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C is a circle centered at O. PT1 and PT2 are the tangents drawn from a point P outside the circle to the circle. Then which of these is the most appropriate relation.

C is a circle centered at O. $P T_{1}$ and $P T_{2}$ are the tangents drawn from a point P outside the circle to the circle. Then which of these is the most appropriate relation.