# RD Sharma Class 9 Chapter 16 Solutions (Circles)

RD Sharma Class 9 Maths Solutions Chapter 16 is the perfect reference book for a thorough revision of the chapter ‘Circles’. The RD Sharma Solutions Class 9 Maths Chapter 16 Circles consists of 6 exercises – Exercise 16.1, 16.2, 16.3, 16.4., 16.5 and very short answer questions. There are in total of 33 problems in Chapter 16 Circles. These problems cover various concepts and theories related to Circles.

Practising different types of questions is necessary so you can solve any question that might be asked in the examination. RD Sharma Class 9 Maths Solutions Chapter 16 Circles can be the ultimate practice book for you. It consists of different types of tricky questions covering different concepts related to Circles. Practising these questions will give you a better grasp over the chapter.

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## Important topics for RD Sharma Class 9 Maths Solutions Chapter 16 Circles

- According to RD Sharma Class 9 Maths Chapter 16, a circle is the collection of all points in a plane. These points should be equidistant from a fixed point in the plane.
- You will get to know that equal chords of a circle subtend equal angles at the centre.
- The chapter also clarifies the theorem that if the angles subtended by two chords of a circle at the centre are equal, then the chords are also equal.
- The perpendicular from the centre of a circle to a chord bisects the chord.
- The line which is drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
- Only one circle can pass through three non-collinear points.
- Equal chords of a circle are equidistant from the centre.
- Chords which are equidistant from the centre of a circle are equal.
- If the two arcs of a circle are incongruence, then their corresponding chords are equal and conversely, if the two chords of a circle are equal, then their corresponding arcs are congruent.
- The congruent arcs of a circle subtend equal angles at the centre.
- The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- Angles which are in the same segment of a circle are equal.
- Angles in a semicircle form an angle of 90 degrees.
- If a line segment joining two points subtends equal angles at two other points lying on the sane side of the line containing the line segment, the four points lie on a circle.
- The sum of both the pair of opposite angles of a cyclic quadrilateral is 180 degrees.
- If the sum of a pair of opposite angles of a quadrilateral is 180 degrees, the quadrilateral is cyclic.

### Exercise discussion for RD Sharma Class 9 Maths Solutions Chapter 16 Circles

- The first exercise – Exercise 16.1 has two questions.
- The first question is in the form of fill in the blanks.
- The second question is in the form of true and false statements.
- All these questions are based on your knowledge of the concepts given in the chapter.
- There are seven questions in Exercise 16.2.
- Question 1 to 4 needs you to find either the radius or the length of the cord or the distance of a point from the centre of the circle.
- Question 5 wants you to give a method of finding the centre of the circle.
- 6th and 7th questions are proof-based questions.
- There are again just 2 questions in exercise 16.3.
- These two questions are statement based and involve a few complicated calculations.
- Exercise 16.4 has six questions.
- 1 to 4th question involves finding a specific angle within the circle.
- Question 5th to 7th is proof-based questions.
- Exercise 16.5 has eleven questions.
- Question 1st to 4th need you to find the angles.
- Question 5th is a proof-based question.
- Question 6th to 11th questions need you to find specific angles.
- There are 4 VSAQs in total.
- These VSAQs are quite easy and involve finding the angles.

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