Class 6 Exam > Class 6 Questions > Which of the following statements is false?a)...
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Which of the following statements is false?
- a)Every chord of a circle is also a diameter.
- b)The centre of a circle is always in its interior.
- c)Every diameter of a circle is also a chord.
- d)Two diameters of a circle will necessarily intersect.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements is false?a)Every chord of a circle i...
False Statement: Every chord of a circle is also a diameter.
- Understanding Chords and Diameters:
- Explanation of the False Statement:
- Counterexample:
- Conclusion:
- A chord of a circle is a line segment that connects two points on the circumference of the circle.
- A diameter of a circle is a chord that passes through the center of the circle.
The false statement suggests that every chord of a circle is also a diameter. However, this is not true. Let's understand why:
A counterexample is a specific example that disproves a statement. In this case, we can provide a counterexample where a chord is not a diameter:
Let's consider a circle with center O and two points A and B on its circumference. Segment AB is a chord of the circle.
___________O___________
/ \
/ \
/ \
/ \
A B
In this case, segment AB is a chord of the circle but it is not a diameter. The diameter of the circle would be a line segment passing through the center O and having endpoints on the circumference of the circle.
Therefore, the false statement is that every chord of a circle is also a diameter. In reality, a chord can be any line segment connecting two points on a circle, whereas a diameter is a specific chord that passes through the center of the circle.
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Which of the following statements is false?a)Every chord of a circle i...
To determine the false statement:
- A: Every chord of a circle is not always a diameter.
- B: The center of a circle is indeed always in its interior.
- C: Every diameter of a circle is indeed also a chord.
- D: Two diameters of a circle will never intersect; they are parallel.
The false statement is A: "Every chord of a circle is also a diameter." This is untrue because a chord may or may not pass through the center of a circle, unlike a diameter.
- A: Every chord of a circle is not always a diameter.
- B: The center of a circle is indeed always in its interior.
- C: Every diameter of a circle is indeed also a chord.
- D: Two diameters of a circle will never intersect; they are parallel.
The false statement is A: "Every chord of a circle is also a diameter." This is untrue because a chord may or may not pass through the center of a circle, unlike a diameter.
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Which of the following statements is false?a)Every chord of a circle is also a diameter.b)The centre of a circle is always in its interior.c)Every diameter of a circle is also a chord.d)Two diameters of a circle will necessarily intersect.Correct answer is option 'A'. Can you explain this answer?
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