Question

Calculate the length of tangent from a point 15 cm away from the centre of a circle of radius 9 cm.

• A. 11 m
• B. 9 m
• C. 12 m
• D. 10 m

Answer 1

The Correct Option is C

To solve the problem, we need to find the length of a tangent drawn from a point 15 cm away from the center of a circle with radius 9 cm.

1. Understanding the Geometry:
The situation forms a right-angled triangle with:
- Hypotenuse = distance from the external point to the center = 15 cm
- One leg = radius of the circle = 9 cm
- Other leg = length of the tangent (to be found)

2. Applying the Pythagoras Theorem:
Let $L$ be the length of the tangent. Then:
$ L^2 = 15^2 - 9^2 = 225 - 81 = 144 $

3. Solving for $L$:
$ L = \sqrt{144} = 12 $ cm

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