Which of the following statements is INCORRECT?

Options

A. Things which coincide with one another are equal to one another.
B. Two distinct lines can have more than one point in common.
C. A circle can be drawn with any centre and any radius.
D. A straight line may be drawn from any one point to any other point.

Answer

To determine which statement is incorrect, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** "Things which coincide with one another are equal to one another."

- **Explanation:** When two points or objects coincide, it means they occupy the same space or position. Therefore, if two points coincide, they are indeed equal.
- **Conclusion:** This statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement:** "Two distinct lines can have more than one point in common."

- **Explanation:** By definition, distinct lines are lines that are not the same. If two lines are distinct, they can either be parallel (which means they do not intersect at all) or they can intersect at exactly one point. Therefore, it is impossible for two distinct lines to have more than one point in common.
- **Conclusion:** This statement is **incorrect**.

### Step 3: Analyze the Third Statement
**Statement:** "A circle can be drawn with any center and any radius."

- **Explanation:** A circle is defined as the set of all points that are a fixed distance (the radius) from a central point (the center). Thus, it is indeed possible to draw a circle with any chosen center and radius.
- **Conclusion:** This statement is **correct**.

### Step 4: Analyze the Fourth Statement
**Statement:** "A straight line may be drawn from any one point to any other point."

- **Explanation:** A straight line is defined as the shortest distance between two points. Therefore, it is possible to draw a straight line connecting any two distinct points.
- **Conclusion:** This statement is **correct**.

### Final Conclusion
The **incorrect statement** among the given options is the second statement: "Two distinct lines can have more than one point in common."

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