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A _________ is a simple closed curve all of whose points are at the same distance from a fixed point.
- a)diameter
- b)radius
- c)triangle
- d)circle
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A _________ is a simple closed curve all of whose points are at the sa...
A Circle
A circle is a simple closed curve all of whose points are at the same distance from a fixed point. In other words, it is a two-dimensional geometric figure that is perfectly round and consists of all points in a plane that are equidistant from a fixed center point. The fixed point is called the center of the circle, and the distance from the center to any point on the circle is called the radius.
Properties of a Circle
1. Diameter: The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on the circumference. It is the longest chord of the circle and is twice the length of the radius.
2. Radius: The radius of a circle is a straight line segment that connects the center of the circle to any point on its circumference. All radii of a circle are equal in length.
3. Circumference: The circumference of a circle is the distance around its outer edge. It is calculated using the formula C = 2πr, where C is the circumference and r is the radius.
4. Area: The area of a circle is the measure of the region enclosed by its circumference. It is calculated using the formula A = πr^2, where A is the area and r is the radius.
Why the Correct Answer is 'Circle'
In this question, we are given a simple closed curve where all points are at the same distance from a fixed point. This description matches the properties of a circle. A circle is the only geometric figure that satisfies this condition. The other options, such as diameter, radius, and triangle, do not meet the requirement of being a simple closed curve with all points equidistant from a fixed point. Therefore, the correct answer is option 'D' - circle.
Conclusion
A circle is a fundamental geometric shape that is defined as a simple closed curve where all points are at the same distance from a fixed point. It is important to understand the properties of a circle, such as the radius, diameter, circumference, and area, to solve problems related to circles in mathematics and other fields.
A circle is a simple closed curve all of whose points are at the same distance from a fixed point. In other words, it is a two-dimensional geometric figure that is perfectly round and consists of all points in a plane that are equidistant from a fixed center point. The fixed point is called the center of the circle, and the distance from the center to any point on the circle is called the radius.
Properties of a Circle
1. Diameter: The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on the circumference. It is the longest chord of the circle and is twice the length of the radius.
2. Radius: The radius of a circle is a straight line segment that connects the center of the circle to any point on its circumference. All radii of a circle are equal in length.
3. Circumference: The circumference of a circle is the distance around its outer edge. It is calculated using the formula C = 2πr, where C is the circumference and r is the radius.
4. Area: The area of a circle is the measure of the region enclosed by its circumference. It is calculated using the formula A = πr^2, where A is the area and r is the radius.
Why the Correct Answer is 'Circle'
In this question, we are given a simple closed curve where all points are at the same distance from a fixed point. This description matches the properties of a circle. A circle is the only geometric figure that satisfies this condition. The other options, such as diameter, radius, and triangle, do not meet the requirement of being a simple closed curve with all points equidistant from a fixed point. Therefore, the correct answer is option 'D' - circle.
Conclusion
A circle is a fundamental geometric shape that is defined as a simple closed curve where all points are at the same distance from a fixed point. It is important to understand the properties of a circle, such as the radius, diameter, circumference, and area, to solve problems related to circles in mathematics and other fields.
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A _________ is a simple closed curve all of whose points are at the sa...
Circle
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A _________ is a simple closed curve all of whose points are at the same distance from a fixed point.a)diameterb)radiusc)triangled)circleCorrect answer is option 'D'. Can you explain this answer?
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