A tangent is drawn to a circle of radius 6 cm from a point situated at a distance of 10 cm from the centre of the circle the length of the tangent will be

Options

A. `7 cm`
B. `4 cm`
C. `5 cm `
D. `8 cm`

Answer

To find the length of the tangent drawn from a point outside the circle to the circle, we can use the Pythagorean theorem.

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius of the circle (r) = 6 cm
- Distance from the center of the circle to the external point (d) = 10 cm

2. **Understand the relationship:**
- When a tangent is drawn from an external point to a circle, it forms a right triangle with the radius and the distance from the center to the external point.
- Let the length of the tangent be denoted as \( PT \).

3. **Apply the Pythagorean theorem:**
- In the right triangle formed, we have:
\[ OP^2 = OT^2 + PT^2 \]
- Here, \( OP \) is the distance from the center to the external point (10 cm), \( OT \) is the radius of the circle (6 cm), and \( PT \) is the length of the tangent we want to find.

4. **Substituting the known values:**
- Substitute \( OP = 10 \) cm and \( OT = 6 \) cm into the equation:
\[ 10^2 = 6^2 + PT^2 \]
- This simplifies to:
\[ 100 = 36 + PT^2 \]

5. **Isolate \( PT^2 \):**
- Rearranging gives:
\[ PT^2 = 100 - 36 \]
\[ PT^2 = 64 \]

6. **Calculate \( PT \):**
- Taking the square root of both sides:
\[ PT = \sqrt{64} = 8 \text{ cm} \]

### Final Answer:
The length of the tangent is **8 cm**.