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Which of the following is a false statement?
- a)Infinitely many chords can be drawn in a circle.
- b)A semicircle is an arc of the circle.
- c)The diameter of a circle passes through its centre.
- d)The line joining any two points on a circle is called its diameter.
Correct answer is option 'D'. Can you explain this answer?
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Which of the following is a false statement?a)Infinitely many chords c...
A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
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Which of the following is a false statement?a)Infinitely many chords c...
False Statement: The line joining any two points on a circle is called its diameter.
Explanation:
A circle is a closed curve in which all points are equidistant from a fixed point called the center. In a circle, there are several important elements such as the radius, diameter, chord, and arc.
Definition of a Diameter:
A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest chord in a circle and its length is twice the length of the radius.
Explanation of the False Statement:
The false statement in this question is option 'D', which states that the line joining any two points on a circle is called its diameter. This statement is incorrect because a diameter specifically refers to a chord that passes through the center of the circle.
Explanation of the True Statements:
a) Infinitely many chords can be drawn in a circle:
This statement is true. A chord is a line segment with its endpoints on the circle. Since there are infinitely many points on the circumference of a circle, there are infinitely many possible chords that can be drawn.
b) A semicircle is an arc of the circle:
This statement is true. A semicircle is a half of a circle. It is formed by drawing a diameter and considering the arc connecting the endpoints of the diameter. The diameter itself divides the circle into two equal halves, each of which is a semicircle.
c) The diameter of a circle passes through its center:
This statement is true. The diameter is a line segment that passes through the center of the circle. It divides the circle into two equal halves, and any point on the diameter is equidistant from the circumference of the circle.
To summarize, the false statement is option 'D' which incorrectly states that the line joining any two points on a circle is called its diameter. The other statements (a, b, and c) are true and accurately define the properties of a circle and its elements.
Explanation:
A circle is a closed curve in which all points are equidistant from a fixed point called the center. In a circle, there are several important elements such as the radius, diameter, chord, and arc.
Definition of a Diameter:
A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest chord in a circle and its length is twice the length of the radius.
Explanation of the False Statement:
The false statement in this question is option 'D', which states that the line joining any two points on a circle is called its diameter. This statement is incorrect because a diameter specifically refers to a chord that passes through the center of the circle.
Explanation of the True Statements:
a) Infinitely many chords can be drawn in a circle:
This statement is true. A chord is a line segment with its endpoints on the circle. Since there are infinitely many points on the circumference of a circle, there are infinitely many possible chords that can be drawn.
b) A semicircle is an arc of the circle:
This statement is true. A semicircle is a half of a circle. It is formed by drawing a diameter and considering the arc connecting the endpoints of the diameter. The diameter itself divides the circle into two equal halves, each of which is a semicircle.
c) The diameter of a circle passes through its center:
This statement is true. The diameter is a line segment that passes through the center of the circle. It divides the circle into two equal halves, and any point on the diameter is equidistant from the circumference of the circle.
To summarize, the false statement is option 'D' which incorrectly states that the line joining any two points on a circle is called its diameter. The other statements (a, b, and c) are true and accurately define the properties of a circle and its elements.
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Which of the following is a false statement?a)Infinitely many chords can be drawn in a circle.b)A semicircle is an arc of the circle.c)The diameter of a circle passes through its centre.d)The line joining any two points on a circle is called its diameter.Correct answer is option 'D'. Can you explain this answer?
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Which of the following is a false statement?a)Infinitely many chords can be drawn in a circle.b)A semicircle is an arc of the circle.c)The diameter of a circle passes through its centre.d)The line joining any two points on a circle is called its diameter.Correct answer is option 'D'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Which of the following is a false statement?a)Infinitely many chords can be drawn in a circle.b)A semicircle is an arc of the circle.c)The diameter of a circle passes through its centre.d)The line joining any two points on a circle is called its diameter.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is a false statement?a)Infinitely many chords can be drawn in a circle.b)A semicircle is an arc of the circle.c)The diameter of a circle passes through its centre.d)The line joining any two points on a circle is called its diameter.Correct answer is option 'D'. Can you explain this answer?.
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