Question

The length of the tangent from a point 15 cm away from the centre of a circle of radius 9 cm is:

• A. 15 cm
• B. 13 cm
• C. 11 cm
• D. 12 cm

Hint:

To find the length of a tangent from a point outside the circle, use the formula \(\sqrt{d^2 - r^2}\), where \(d\) is the distance from the point to the center and \(r\) is the radius of the circle.

Answer 1

The Correct Option is C

The length of the tangent from a point outside a circle to the point of contact is given by the formula: \[ \text{Length of tangent} = \sqrt{\text{Distance from point to center}^2 - \text{Radius}^2} \] Substituting the given values: \[ \text{Length of tangent} = \sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12 \, \text{cm} \] Thus, the correct answer is option (4).