Which of the following is Euclid's third postulate ?

Options

A. A straight line may be drawn from any one point to any other point.
B. A terminated line can be produced infinitely.
C. A circle can be drawn with any centre and any radius.
D. All right angles are equal to one another.

Answer

To determine which of the following is Euclid's third postulate, we need to analyze the options provided and identify the correct statement based on Euclid's original postulates.

### Step-by-Step Solution:

1. **Understanding Euclid's Postulates**: Euclid proposed five fundamental postulates in his work "Elements". We need to recall what each postulate states.

2. **Identifying the First Postulate**: The first postulate states that a straight line can be drawn from any one point to any other point. This is not the third postulate.

3. **Identifying the Second Postulate**: The second postulate states that a terminated line can be extended indefinitely in both directions. This is also not the third postulate.

4. **Identifying the Fourth Postulate**: The fourth postulate states that all right angles are equal to one another. This is not the third postulate either.

5. **Identifying the Third Postulate**: The third postulate states that a circle can be drawn with any center and any radius. This is the correct statement for the third postulate.

6. **Conclusion**: Based on the analysis, the statement that corresponds to Euclid's third postulate is: "A circle can be drawn with any center and any radius."

### Final Answer:
The correct answer is option 3: "A circle can be drawn with any center and any radius."

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