A tangent is drawn from a point P which is at a distance of 10 cm from the centre of the circle O. The radios of the circle is 6 cm. Then the length of portion of tangent between P and the point of contact is:

8 cm

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9 cm

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12 cm

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5 cm

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Solution

The correct option is A 8 cm
The angle between the radius and the tangent at a point is $90^{\circ}$ .
Let, the point of contact be A, $Δ O A P$ is a right triangle.

$⟹ (O A)^{2} + (A P)^{2} = (O P)^{2}$
$⟹ (A P)^{2} = (O P)^{2} - (O A)^{2}$
$⟹ (A P)^{2} = (10)^{2} - (6)^{2}$
$⟹ A P = 8 c m$

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A tangent is drawn from a point P which is at a distance of 10 cm from the centre of the circle O. The radios of the circle is 6 cm. Then the length of portion of tangent between P and the point of contact is:

The correct option is A 8 cmThe angle between the radius and the tangent at a point is 90∘. Let, the point of contact be A, ΔOAP is a right triangle. ⟹(OA)2+(AP)2=(OP)2 ⟹(AP)2=(OP)2−(OA)2 ⟹(AP)2=(10)2−(6)2 ⟹AP=8 cm