Free download NCERT Solutions for Class 9 Maths Chapter 10 circles exercise 10.1, 10.2, 10.3, 10.4, 10.5 and 10.6 in PDF form. Class 9 Maths Solutions along with the other subjects NCERT Solutions are available in PDF form to free download.

## NCERT Solutions for Class 9 Maths Chapter 10

### Class 10 Maths Chapter 10 – Circles

#### Important Questions With Answers

- If the sum of a pair of opposite angles of a quadrilateral is 180°, then quadrilateral is ___________. [Answer: Cyclic Quadrilateral]
- A round pizza is cut into 4 equal pieces. What does each piece represent? [Answer: Sector]
- AD is a diameter of a circle and AB is a chord if AD = 34 cm, AB = 30 cm then find the distance of AB from the centre of chord. [Answer: 8 cm]
- Given two concentric circles with centre O. A line cut the circle at A, B, C and D respectively. If AB = 10 cm, then find the length of CD. [Answer: 10 cm]
- Diameter is the _________ Chord of a circle. [Answer: longest]
- Circle having the same centre and different radii are called __________ circles. [Answer: Concentric]
- Prove that cyclic parallelogram is a rectangle.
- A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. [Answer: 30°, 150°]
- If two non-parallel sides of a trapezium are equal prove that it is cyclic quadrilateral.
- In an equilateral triangle, prove that the centroid and the circumcentre coincide.
- If two equal chords of a circle intersect within the circle prove that the segment of one chord is equal to corresponding segment of other chord.
- Prove that if a pair of opposite angles of a quadrilateral is supplementary then the quadrilateral is cyclic.
- Bisector of angle A, B and C of a ∆ABC intersect its circumcircle at D, E and F respectively, prove that the angles of a triangle DEF are 90° – ½A, 90° – ½B and 90° – ½C.
- Find the sum of the angles in the four segments exterior to a cyclic quadrilateral. [Answer: 540°]
- Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that angle ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre. Angle ABC = ½[angle DOE – angle AOC]
- During a practical activity in maths lab students were using circular geo board. The angle subtended by an arc at the centre is (2a + 50°). Pallavi calculated BAC as (a + 25°). a) Is her finding correct? Justify it. b) Find angle BAC if a = 30° c) What will be the value of angle BOC for a=15° d) Which values are depicted here? [Answer: (i) yes, (ii) 55°, (iii) 80° (iv) Truth, Scientific temper]
- Three friends ordered 3 pizzas of the same sized for them. Just then two more friends joined them. They decided to share 3 pizzas among all of them. a) Find the area of the share of pizza each child gets if the radius of each pizza is 7 cm. b) Which values of children are depicted here? [Answer: (a) 92.4 cm², (b) Cooperation]