The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from a point oat a distance of 10 cm from its centre.

Options

A. 7cm
B. 5cm
C. 6cm
D. 4cm

Answer

To solve the problem of finding the length of the tangent drawn to a circle from a point outside the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the circle (r) = 8 cm
- Distance from the center of the circle to the point (d) = 10 cm

2. **Visualize the Problem:**
- Draw a circle with center O and radius 8 cm.
- Mark point P outside the circle such that the distance OP = 10 cm.

3. **Draw the Tangent:**
- Draw a tangent line from point P that touches the circle at point T.
- The radius OT is perpendicular to the tangent PT at point T.

4. **Use the Pythagorean Theorem:**
- In triangle OPT, we have:
- OP = d = 10 cm (hypotenuse)
- OT = r = 8 cm (one leg)
- PT = x (the length of the tangent we need to find, the other leg)

5. **Set Up the Equation:**
- According to the Pythagorean theorem:
\[ OP^2 = OT^2 + PT^2 \]
Substituting the known values:
\[ 10^2 = 8^2 + x^2 \]

6. **Calculate the Squares:**
- Calculate \(10^2\) and \(8^2\):
\[ 100 = 64 + x^2 \]

7. **Rearrange the Equation:**
- Solve for \(x^2\):
\[ x^2 = 100 - 64 \]
\[ x^2 = 36 \]

8. **Find the Length of the Tangent:**
- Take the square root of both sides:
\[ x = \sqrt{36} = 6 \text{ cm} \]

9. **Conclusion:**
- The length of the tangent drawn from point P to the circle is 6 cm.

### Final Answer:
The length of the tangent drawn to the circle from point P is **6 cm**.