# Xam Idea Class 10 Maths Chapter 8 Solutions: Circles

Xam Idea Class 10 Maths Solutions for Chapter 8 ‘Circles’ provide you with all the important questions and solutions of the chapter with a step by step and detailed explanation. The solutions for Xam Idea Class 10 Maths Solutions for Chapter 8 Circles will help you to revise the whole chapter in minutes and also contain the best tips for preparation of the exam. The solutions will help you to understand the chapter in an effective way. You will be aware of the questions that are important from the board exam point of view.

Xam Idea Class 10 Maths Solutions covers all the crucial topics of the chapter such as the basics of the circle, how to draw a tangent to a circle, how to find the length of tangents and theorems and their proof. There are also questions related to tangents and their lengths. The chapter contains 6 exercises with 50 questions. The exercises contain a mixture of questions such as very short answer type questions, long answer questions, HOTS etc. All the solutions are formed as per the latest guidelines proposed by CBSE. Xam Idea Solutions act as one of the most helpful resources of study and by opting for them you are making a smart preparation plan for your board exams.

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## Important Topics In The Xam Idea Class 10 Maths Solutions Chapter 8: Circles

The Chapter starts with a very important definition of a circle and then covers all the terms related to circles and their properties such as radius, diameter, arc, chord, secant, segment etc. You will also learn more about the concept of a tangent, the utility or need of tangent and many theorems related to tangents whose results we will use in the exercise. The vice versa of the theorems and their proofs are also important to understand the chapter in a detailed manner.

**Introduction**

- A circle is a collection of all the points in a plane which are at constant/fixed distance from a particular point and that fixed point is called the centre. When all the points are joined with each other and not from the centre they form a circle.
- The constant/fixed distance from the centre with all the other points is called the radius.
- A line joining any two points in a circle is called a chord. A chord passing through the centre of the circle is called the diameter. It is the longest chord.
- The length of the boundary or the perimeter of the circle is called the circumference of the circle.
- An arc is the part of the circle joining two points on the circumference or length of the boundary of the circle
- An area made by an arc and two radii of the circle is called a sector.
- An area made by a chord and an arc of the circle is called a segment.
- If a line and circle have no common points then that line is called a non- intersecting line with respect to the circle.
- When a line intersects the circle in such a way that there are two common points then it is called a secant.

**Tangent To A Circle**

- When a line touches the circle in such a way that they have only one common point and that line forms 90 degrees on that common point then that line is called a Tangent and that common point is called a point of contact.
- All the tangents of the circle are perpendicular to the radius through the point of contact of that tangent.
- There could be only one tangent at one point of contact.
- Tangent could not be drawn from any point inside the circle because if the tangent is inside then it will not be considered as a tangent.
- There could be only two tangents to a circle from any point outside the circle and that tangents will meet after some distance,
- The length of all the tangents drawn from an external point or any point outside the circle are equal.
- The tangent to a circle can be seen as a special case of the secant when the two endpoints of its corresponding chord coincide.
- There are exactly two tangents which are parallel to each other and touch the circle at two diametrically opposite points.

**Theorems Related To a Tangent Of Circle**

**Theorem 1:**In this theorem, you will learn that if there is a tangent to a circle then that tangent will be perpendicular to the radius. The tangent can be drawn at any point on the circle. Tangent forms 90 degrees at the point of contact. We have given a circle with centre O and a tangent XY to the circle at a point P then OP is perpendicular to XY.**Theorem 2:**This theorem will explain to you that if two tangents are drawn from a point which is outside the circle then the tangents drawn from that external point are equal. As they are drawn from the same point, the length of the tangents is equal. We have a circle with centre O a point P lying outside the circle and two tangents PQ and PR on the circle from P then PQ= PR

### Exercise Discussion Of Xam Idea Class 10 Maths Solutions Chapter 8 Circles

**Very Short Answer Type Questions**

There are a total of 12 questions in this section where you have to answer in a few words only. In the questions, you will be given radius and some other distance or angle and you have to find the length of tangent or the angle formed by the tangent at the centre. It also includes questions like you will have a set of length and you have to tell which is the correct measurement of the tangent with the help of figures.

**Short Answer Type Questions-I**

This section has a total number of 12 questions in which you have to find the length of a tangent with the clue given in the statement or you can have questions like prove that a line segment joining the points of contact of the two parallel tangents of a circle passes through the centre, or you have to prove tangents equal etc.

**Short Answer Type Questions-II**

This section includes 12 questions in all where you have to make the figure or draw the tangents with the help of statement and then answer about their lengths. In this, you can also find questions like prove that tangents drawn at the ends of a diameter of a circle are parallel or you have to find the length of the common chord etc.

**Long Answer Type Questions**

This section has a total number of 7 questions in which you have to proof the theorems or prove that a parallelogram circumscribing a circle is a rhombus. All the questions are based on the tangent concept and are a little bit longer as well.

**HOTS (High Order Thinking Skills)**

This section includes only 4 questions which are a little bit tricky such as you have to prove the opposite sides of a quadrilateral circumscribing a circle subtend equal angles at the centre or you have to draw the figure from the question and then have to apply all the concept that you read in the chapter.

**Value-Based Questions**

This section contains 3 questions and you just have to apply the result of theorems in these questions. In addition, you have to look at which value is described in the question.

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- Our Xam Idea Solutions for Class 10 Maths Chapter 8 Circles will actually resolve all your doubts and problems related to the chapter.
- Our solutions are based on the latest CBSE Class 10 Maths syllabus and exam pattern.