From a point Q, the length of the tangent to a circle is 24 cm and

Question:

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(a) 7 cm

(b) 12 cm

(c) 15 cm

(d) 24.5 cm

Solution:

Let us first put the given data in the form of a diagram.

The given data is as follows:

QP = 24 cm

QO = 25 cm

We have to find the length of OP, which is the radius of the circle.

We know that the radius of a circle will always be perpendicular to the tangent at the point of contact. Therefore, OP is perpendicular to QP. We can now use Pythagoras theorem to find the length of QP.

$O P^{2}=O Q^{2}-Q P^{2}$

$O P^{2}=25^{2}-24^{2}$

$O P^{2}=(25+24)(25-24)$

$O P^{2}=49$

$O P=\sqrt{49}$

 

$O P=7$

Therefore the length of the radius of the circle is 7 cm.

Hence the correct answer to the question is choice (a).

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