RS Aggarwal Class 10 Chapter 8 Solutions (Circles)
RS Aggarwal Solutions for Class 10 Maths Chapter 8 ‘Circles’ contain all the important summaries and explanations that you need to work upon. In this chapter of RS Aggarwal Class 10 Maths Solutions, you shall learn to solve different problems based on circles, alongside the concept of secant, tangent to the circle, length of a tangent and number of tangents to a circle. This chapter will also help you to understand some important theorems on circle tangents.
In this chapter, there are 31 problems divided into 2 exercises. All the exercise questions are in sync with the latest CBSE Class 10 Maths syllabus and will immensely help you in your board exams. By solving these questions, you will be able to find the length of the tangent drawn from a point away from the radius of the circle, length of chords of concentric circles, length of chords of a circle inscribing a quadrilateral.
Instasolv’s RS Aggarwal Class 10 Maths Solutions for Chapter 8 ‘Circles’ are well structured to improve your concept-based knowledge. These solutions will instil the confidence in you and you will be able to solve the various types of questions that may occur on the board exam. Whether it be finding the area of circular regions or questions related to sectors and segments of a circle, these solutions will help you prepare every topic of the chapter thoroughly.
Important Topics for RS Aggarwal Solutions for Class 10 Maths Chapter 8 –Circles
- Circle: It is the collection of points within a plane at a constant distance from a fixed point.
- Centre: It is said to be a fixed point within a circle that is equidistant from all other points on the boundaries of the circle.
- Radius: It is a constant distance from the centre of the circle to the boundaries or circumference of the circle.
- Chord: A line segment joining any two points on a circle is called a chord.
- Diameter: A chord passing through the centre of the circle is called the diameter. It is the longest chord.
Circle and a Line within a Plane :
- They may be non-intersecting.
- They might have only one common point – in such cases, the line tends to touch the circle.
- They may have only two common points – such a case involves the line cutting the circle.
- A tangent to a circle confirms as a line that touches the circle at a single point. Each point on the circle comprises a unique tangent passing through it.
- Secant to a circle is a line that has two points in common with the circle. It cuts the circle at two points that define a chord of the circle.
- Tangent” as a special case of Secant.
- For each given secant of a circle, there are exactly two tangents that might be parallel to it and touch the circle at two diametrically opposite points.
- Theorem: The tangent to the circle at any factor is perpendicular to the radius of the circle that passes via that point of contact. Consider the figure below. Here, O is the centre and OP⊥XY.
- Theorem: If the point is within an interior region of the circle, then a line passing through that point is said to be a secant. So, none of the tangents can be drawn to a circle that passes through a point that lies inside it.
- Tangents to a circle from an Internal Point:
Whenever a point of tangency stays on the circle, there is exactly a single tangent to a circle that passes across it.
- Tangents to a circle from an External Point:
When the point lies outside of the circle, there are accurately two tangents to a circle through it
- Length of a Tangent
The length of the tangent from the factor (Say P) to the circle is described as the segment of the tangent from the outside point P to the point of tangency I with the circle. In this case, PI is the tangent period
- When two tangents drawn through any external point to a circle are of the same length. Here, PT1=PT2
Exercise discussion for RS Aggarwal Class 10 Maths Solutions for Chapter 8 –Circles
It has 16 questions where you have to solve various problems based on the circle and its parts, for example, the concept of secant, tangent and other important theorems of this chapter.
It has 15 questions which mainly focus on vital problems based on tangent theorems that are high weightage questions from exam point of view. Many questions related to proving the theorems of the chapter are also included in the exercises.
In the end, there are 55 multiple choice questions in the chapter based on the various concepts of the chapter. They enable you to practice the theoretical concepts of the chapter easily.
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