One chord of a circle is known to be 10.1 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 find the radius of a circle given that one chord is 10.1 cm, we can follow these steps:

### Step 1: Understand the relationship between a chord and the radius
A chord of a circle is a line segment with both endpoints on the circle. The longest chord of a circle is the diameter. The radius is half of the diameter.

### Step 2: Consider the case where the chord is the diameter
If the given chord (10.1 cm) is the diameter, then we can calculate the radius as follows:
\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{10.1 \text{ cm}}{2} = 5.05 \text{ cm} \]

### Step 3: Determine the implications of the chord length
Since the chord can be shorter than the diameter, the radius must be greater than half the length of the chord. Therefore, if the chord is not the diameter, the radius must be greater than 5.05 cm.

### Step 4: Conclusion
Thus, the radius of the circle must be greater than 5.05 cm.

### Final Answer
The radius of the circle must be greater than 5.05 cm.

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