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  • 1. 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

1. 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

Answers (1)

best_answer

The correct option is (A) = 7 cm
Given that,
The length of the tangent (QT) is 24 cm and the length of OQ is 25 cm .
Suppose the length of the radius OT is $l \mathrm{~cm}$.
We know that $\triangle O T Q$ is a right-angle triangle. So, by using Pythagoras theorem-
$O Q^2=T Q^2+O T^2$
$l=\sqrt{25^2-24^2}$
$O T=l=\sqrt{49}$
$\text { OT }=7 \mathrm{~cm}$

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manish

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