RS Aggarwal Class 6 Solutions Chapter-18 Circles

18.1 Introduction

Class 6 RS Aggarwal Maths Chapter 18 deals with circles and their important concepts. A circle is a shape consisting of all points in a plane that are a length from a given point, the center; similarly, it is the curve traced by a point that travels in a plane such that its distance is constant from a given point. The radius is called the distance between every point on the circumference of the circle and its center. A circle may be thought of like a hula hoop. The circle is just those points on the circumference. The points are not part of the circle inside the hula hoop and are considered interior points. A circle is 360° in the same way. A circle can be broken into smaller parts. An arc is called a portion of a circle and an arc is labeled according to its angle. Arcs are split into small arcs (0 ° < v < 180 °), wide arcs (180 ° < v < 360 °) and semicircles (v = 180 °). Central angles are created when the diameters converge in the middle of the circle. You start your pieces in the middle, just like when you cut a pizza. The number of vertices in a circle is zero and so are the faces.

18.2 Basic Definitions

• Circle: In a plane whose distance from a fixed point remains constant, a circle is a sequence of all those points.

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• Radius: The circle radius is the length of the line segment that connects the middle of the circle with every point across its circumference.

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• Diameter: The diameter of the circle is considered a straight line going through the middle of a circle with each of its ends at the circumference of a circle. 

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• Chord: The chord of the circle is called a line segment with its end-points lying on a circle. A chord, by definition, is a straight line connecting the circumference of a circle with 2 ends. A circle's diameter is known to be the longest chord since it joins the circumference of a circle to points.

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• Secant: A straight line that cuts a two-point circle. It is called an extended chord as well. A curve secant is a line that intersects the curve at a minimum of two different points. Secant comes from the Latin word secure, which implies to cut. A secant can intersect the circle at exactly two points in the case of a circle.

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• Tangent: A coplanar, straight line at a single point touching the circle. In geometry, the straight line that "just touches" the curve at that point is the tangent line (or simply tangent) to a plane curve at a given point.

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• Arc: The arc is a part of a circle's circumference. 

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• Sector: A sector is called the section of a circle surrounded by either of two radii and an arc. The sector is said to be part of a globe, along with its two radii, made of the arc of the circle. It is a portion of the circle created at both endpoints of the arc by a portion of the circumference (arc) and radius of the circle. With a slice of cake or a pizza, the shape of a sector of a circle can be contrasted.

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• Segment: Each chord splits a circle into two sections, which are called segments. 

The main section includes a circle center, but the minor segment does not contain a circle center. 

The smaller portion of a circle is considered the smaller section, and the larger portion is called the main segment.

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Key Features of RS Aggarwal Class 6 Solutions Chapter 18

• The solutions provided are solved by the subject-matter experts at Vedantu. They have designed these solutions in such a way that it is easier for the students to understand and implement them in their practice sessions as well.

• All the solutions are provided in PDF format, so it is easier to access through mobile, pc, or tablet.

Preparation Tips

The circle is a Chapter that plays an important role in academics as it is included in the course syllabus in senior Classes as well. Therefore, it is important to learn this Chapter well and be strong with the basics.  Few things to remember while preparing this topic: 

• Make sure you memorize the theorems properly and always try to draw the figures as per the given data while solving a sum.

• You can go through previous years question papers to understand what kind of questions come in exams.

Conclusion

The circle is a shape that we see at a lot of places but in this Chapter, we will learn a lot of topics that are related to the concept of the circle. The circle is a two-dimensional shape that has no faces, no vertices and no corners or edges. An important relationship that we learn in this Chapter is between the radius and diameter. Several parts of a circle are discussed in the above segment, a few of which are - chord, segment, tangent, etc. It is important to be familiar with these terms as these will help in understanding and solving the sums of this Chapter.