One chord of a circle is known to be 10 cm. The radius of this circle must be

Options

A. 5 cm
B. greater than 5 cm
C. greater than or equal to 5 cm
D. less than 5 cm

Answer

To solve the problem, we need to determine the minimum radius of a circle given that one of its chords is 10 cm long.

### Step-by-Step Solution:

1. **Understanding the Relationship Between Chords and Radius**:
- In a circle, the diameter is the longest chord. Any chord will always be shorter than or equal to the diameter.
- Therefore, if we know the length of a chord, we can infer that the diameter of the circle must be greater than this chord.

2. **Identify the Given Information**:
- The length of the chord (AB) is given as 10 cm.

3. **Establish the Relationship**:
- The diameter (D) of the circle is greater than the length of the chord. Thus, we can write:
\[ D > 10 \text{ cm} \]

4. **Relate Diameter to Radius**:
- The diameter of a circle is twice the radius (R). Therefore, we can express the diameter in terms of the radius:
\[ D = 2R \]

5. **Combine the Inequalities**:
- Since we know that \(D > 10\), we can substitute \(D\) with \(2R\):
\[ 2R > 10 \]

6. **Solve for Radius**:
- To find the minimum radius, divide both sides of the inequality by 2:
\[ R > \frac{10}{2} \]
\[ R > 5 \text{ cm} \]

7. **Conclusion**:
- The radius of the circle must be greater than 5 cm.

### Final Answer:
The radius of the circle must be greater than 5 cm.