From a point Q the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 13 cm The radius of the circle is

7 cm

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6.5 cm

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5 cm

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9 cm

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Solution

The correct option is B 5 cm
It is given that the tangent of circle is 12 cm and distance of Q from the centre is 13 cm.

Since the radius OT is perpendicular to QT, therefore,

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

$\Rightarrow$ $O T^{2} = 13^{2} - 12^{2}$

$\Rightarrow$ $O T^{2} = 169 - 144$

$\Rightarrow$ $O T^{2} = 25$

$\Rightarrow$ $O T = \sqrt{25}$

$\Rightarrow$ $O T = 5 c m$

Hence option C is correct.

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Similar questions

The tangent to a circle from a point outside the circle measures 15cm. The distance of the point from the centre is 12cm. The radius of the circle is

The length of the tangent to a circle from a point outside the circle measures 12 cm. The distance of the point from the centre is 15 cm.
Find the radius of the circle.

Q. Find the length of a tangent drawn from a point

13

cm away from the centre of a circle of radius

12

cm.

Q. Question 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

Q. Question 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

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From a point Q the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 13 cm The radius of the circle is

The correct option is B 5 cmIt is given that the tangent of circle is 12 cm and distance of Q from the centre is 13 cm.Since the radius OT is perpendicular to QT, therefore,OT2=OQ2−QT2⇒OT2=132−122⇒OT2=169−144⇒OT2=25 ⇒OT=√25 ⇒OT=5cmHence option C is correct.