A chord of length 24 units is a distance of 5 units from the centre of a circle then its radius is

Options

A. 5
B. 12
C. 13
D. 10

Answer

To solve the problem, we need to find the radius of the circle given that a chord of length 24 units is at a distance of 5 units from the center of the circle.

### Step-by-Step Solution:

1. **Draw the Circle and Chord**:
- Begin by drawing a circle with center O.
- Draw a chord PQ such that the distance from the center O to the chord PQ is 5 units.

2. **Identify the Midpoint of the Chord**:
- Let M be the midpoint of the chord PQ. Since the chord is 24 units long, each half of the chord (PM and MQ) will be 12 units. Thus, PM = MQ = 12 units.

3. **Draw a Perpendicular from the Center to the Chord**:
- Draw a line segment OM which is perpendicular to the chord PQ. The length of OM is given as 5 units.

4. **Apply the Pythagorean Theorem**:
- In the right triangle OMP, we can apply the Pythagorean theorem. According to the theorem:
\[ OP^2 = OM^2 + PM^2 \]
- Here, OP is the radius (R), OM is the distance from the center to the chord (5 units), and PM is half the length of the chord (12 units).

5. **Substitute the Values**:
- Substitute the known values into the equation:
\[ R^2 = 5^2 + 12^2 \]
- Calculate the squares:
\[ R^2 = 25 + 144 \]

6. **Calculate R^2**:
- Add the values:
\[ R^2 = 169 \]

7. **Find the Radius R**:
- Take the square root of both sides to find R:
\[ R = \sqrt{169} = 13 \]

8. **Conclusion**:
- The radius of the circle is 13 units.

### Final Answer:
The radius of the circle is **13 units**.