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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

Since QT is a tangent to the circle at T and OT is radius,

$$\therefore \ OT ⊥ QT$$

It is given that OQ = 25 cm and QT = 24 cm,

$$\therefore$$ By Pythagoras theorem, we have

$$\Rightarrow OQ^2 \ = \ QT^2 \ + \ OT^2$$
$$\Rightarrow OT^2 \ = \ OQ^2 \ - \ QT^2$$
$$\Rightarrow \ OT^2 \ = \ 25^2 \ - \ 24^2$$
$$\Rightarrow OT^2 \ = \ 49$$

$$\Rightarrow \ OT \ = \ \sqrt{49} \ = \ 7$$

$$\therefore$$ radius of the circle is 7 cm

$$\therefore$$ Option (A) is correct.