Question

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

• A. 12 cm
• B. 9 cm
• C. 10 cm
• D. 15 cm

Answer 1

The Correct Option is A

Step 1: Recall the formula for the length of a tangent.

The length of a tangent from a point \( P \) outside a circle to the point of tangency is given by:

\[ L = \sqrt{d^2 - r^2}, \]

where:

• \( d \) is the distance from the external point \( P \) to the center of the circle, and
• \( r \) is the radius of the circle.

 

Step 2: Substitute the given values.

Here, \( d = 15 \, \text{cm} \) and \( r = 9 \, \text{cm} \). Substituting these into the formula:

\[ L = \sqrt{15^2 - 9^2}. \]

Step 3: Simplify the calculation.

\[ L = \sqrt{225 - 81} = \sqrt{144} = 12 \, \text{cm}. \]

Final Answer: The length of the tangent is \( \mathbf{12 \, \text{cm}} \).