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The locus of the midpoints of the radii of length 16 cm of a circle is
- a)A concentric circle of radius 8 cm
- b)A concentric circle of radius 16 cm
- c)The diameter of the circle
- d)A straight line passing through the centre of the circle
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The locus of the midpoints of the radii of length 16 cm of a circle is...
Circle is defined as a locus of all the points at the same distance from the centre.
The distance of all the midpoints of the radii will be at a distance of 8 cm from the centre
∴ It is also a circle but with radius 8 cm
∴ It is also a circle but with radius 8 cm
Most Upvoted Answer
The locus of the midpoints of the radii of length 16 cm of a circle is...
Locus of Midpoints of Radii
The locus of the midpoints of the radii of a circle is a concentric circle with a radius half of the original circle.
Definition of Locus
A locus is a set of points that satisfy a particular condition or a geometric figure that can be drawn by connecting all the points that satisfy a given condition.
Explanation
1. Definition of Midpoint
The midpoint of a line segment is the point that divides the segment into two equal parts.
2. Midpoint of a Radius
In a circle, the radius is a line segment that joins the center of the circle to any point on its circumference. The midpoint of a radius is the point that divides the radius into two equal parts.
3. Locus of Midpoints
To find the locus of the midpoints of the radii of a circle, we consider all the possible midpoints that can be formed by dividing the radii into two equal parts.
4. Concentric Circle
A concentric circle is a circle that shares the same center as another circle. In this case, the original circle and the locus of midpoints have the same center.
5. Radius of the Locus Circle
Since the midpoints divide the radii into two equal parts, the length of each radius in the locus circle is half of the length of the corresponding radius in the original circle.
6. Conclusion
Therefore, the locus of the midpoints of the radii of a circle is a concentric circle with a radius half of the original circle. In this case, the locus circle will have a radius of 8 cm, which is half of the radius of the original circle (16 cm).
Hence, the correct answer is option 'A', a concentric circle of radius 8 cm.
The locus of the midpoints of the radii of a circle is a concentric circle with a radius half of the original circle.
Definition of Locus
A locus is a set of points that satisfy a particular condition or a geometric figure that can be drawn by connecting all the points that satisfy a given condition.
Explanation
1. Definition of Midpoint
The midpoint of a line segment is the point that divides the segment into two equal parts.
2. Midpoint of a Radius
In a circle, the radius is a line segment that joins the center of the circle to any point on its circumference. The midpoint of a radius is the point that divides the radius into two equal parts.
3. Locus of Midpoints
To find the locus of the midpoints of the radii of a circle, we consider all the possible midpoints that can be formed by dividing the radii into two equal parts.
4. Concentric Circle
A concentric circle is a circle that shares the same center as another circle. In this case, the original circle and the locus of midpoints have the same center.
5. Radius of the Locus Circle
Since the midpoints divide the radii into two equal parts, the length of each radius in the locus circle is half of the length of the corresponding radius in the original circle.
6. Conclusion
Therefore, the locus of the midpoints of the radii of a circle is a concentric circle with a radius half of the original circle. In this case, the locus circle will have a radius of 8 cm, which is half of the radius of the original circle (16 cm).
Hence, the correct answer is option 'A', a concentric circle of radius 8 cm.
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The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer?
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The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer?.
The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus of the midpoints of the radii of length 16 cm of a circle isa)A concentric circle of radius 8 cmb)A concentric circle of radius 16 cmc)The diameter of the circled)A straight line passing through the centre of the circleCorrect answer is option 'A'. Can you explain this answer?.
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