CBSE Class 9 Maths extra questions for Chapter 10 - Circles are provided here with answers. These questions are very useful for the purpose of revising all important concepts given in the chapter. All the questions are very easy and simple which are meant to test your understanding of the concepts and properties related to circles. So, if you want to make preparations for your Maths exam in an easy and effective manner then try to answer all the questions given here. You can also check here some other important resources to help you in preparations of your CBSE Class 9 Maths Exam 2020-2021.
CBSE Class 9 Maths Extra Questions for Chapter 10 - Circles:
1. Every diameter of a circle is also a chord. Is the converse of this statement also true?
Every diameter is a chord because its end points lie on the circumference of the circle. It is the longest chord that passes through the centre of the circle.
But every chord cannot be a diameter because not every chord passes through the centre.
2. State difference between sector and segment of a circle.
A sector is the region between an arc and the two radii, joining the centre to the end points of the arc whereas a segment is the region between a chord of a circle and its associated arc.
3. In the following figure, find the value of ∠ COD if ∠ AOB = 75o and AB = CD.
∠ COD = 75o
Because equal chords of a circle subtend equal angles at the centre.
4. For a quadrilateral to become cyclic quadrilateral, sum of a pair of its opposite angles must be equal to ________.
For a quadrilateral to become cyclic quadrilateral, sum of a pair of its opposite angles must be equal to 180o.
5. How many circles can be drawn passing through three non-collinear points?
One and only one circle can be drawn through three given non-collinear points.
6. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the ________.
If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.
7. In the following figure, ∠ PQR = 100°, P, A and Q are points on a circle with centre O. Find ∠POQ.
∠POQ = 2 ∠PAQ = 2 × 45 = 90o
Because 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.
8. What do you mean by concyclic points?
A set of points lying on the same circle are said to be concyclic points.
9. A trapezium in which non-parallel sides are equal is said to be _______.
A trapezium in which non-parallel sides are equal is said to be cyclic.
10. What will be the angle subtended by the chord at a point on the major arc if the chord is equal to the radius of the circle?
Angle subtended by the chord at a point on the major arc is equal to 30o.
Hint: (i) Each angle of an equilateral triangle = 60o
(ii) Angle subtended by an arc of a circle at the centre is double the angle subtended by it on any part of the circle
Students must go through the latest CBSE Syllabus for Class 9 Maths so that they can prepare according to the contents prescribed by the board.