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.

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Solution

The correct option is A

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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Similar questions

Which of the following stateements is not true ?

(a) If a point P lies inside a circle, no tangent can be drawn to the circle, passing through P.

(b) If a point P lies on the circle, then one and only tangent can eb drawn to the circle at P.

(d) A circle can have more than two parallel tangents, parallel to a given line.

P is a point outside the circle as shown. MP and NP are the tangents are drawn to the circle from this point. Then $△$ OMP $≅$ $△$ ONP.

P

P

P

P T

P A B

O

P A . P B = P T^{2}

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