CBSE Class 9 Maths Circles MCQs

Question. The centre of a circle lies in ________ of the circle.
(a)exterior
(b) interior
(c) boundary
(d) none of these

Question. A point, whose distance from the centre of a circle is greater than its radius lies in of the circle.
(a)exterior
(b) interior
(c) boundary
(d) none of these

Question. The longest chord of a circle is a ________ of the circle.
(a) diameter
(b) semicircle
(c) chord
(d) sector

Question. Segment of a circle is the region between an arc and _______ of the circle.
(a) diameter
(b) semicircle
(c) chord
(d) sector

Question. A circle divides the plane, on which it lies, in parts.
(a) two
(b) three
(c) four
(d) five

Question. Equal chords of a circle subtend ______angles at the centre.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. If the angles subtended by the chords of a circle at the centre are equal, then the chords are________.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. The perpendicular from the centre of a circle to a chord _______ the chord.
(a) trisect
(b) bisect
(c) coincide
(d) none of these.

Question. The line drawn through the centre of a circle to ______ a chord is perpendicular to the chord.
(a) trisect
(b) bisect
(c) coincide
(d) none of these.

Question. There is one and only one circle passing through _______ given non-collinear points.
(a) two
(b) three
(c) four
(d) five

Question. Chords equidistant from the centre of a circle are ______ in length.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. The angle subtended by an arc at the centre is ________ the angle subtended by it at any point on the remaining part of the circle.
(a) half
(b) double
(c) triple
(d) equal

Question. Angles in the same segment of a circle are equal.
(a) half
(b) double
(c) triple
(d) equal

Question. The sum of either pair of opposite angles of a cyclic quadrilateral is ______.
(a) 180º.
(b) 360º
(c) 90º
(d) none of these

Question. If the sum of a pair of opposite angles of a quadrilateral is ______, the quadrilateral is cyclic.
(a) 180º.
(b) 360º
(c) 90º
(d) none of these

Question: Two parallel chords on the same side of the centre of a circle are 10 cm and 24 cm long and their distance apart is 7 cm. The radius of the circle is
a) 13 cm
b) 5 cm
c) 8 cm
d) 7 cm

Question: E  and F are points on a circle O. Point G is inside circle O and point H is outside circle O The degree measure of ∠EHF is
a) cannot be determined from given data
b) greater than 60°
c) 60°
d) less than 60°

Question: The radius of a circle is 14 m, then the circumference of a circle is 
a) 88 m
b) None
c) 616 m
d) 154 m

1. In a circle, the perpendicular from the centre to a chord bisects the chord.

2. In a circle, the line joining the centre to the midpoint of a chord is perpendicular to that chord.

3. In a” circle, equal chords subtend equal angles at the centre.

4. In a circle, chords which subtend equal angles at the centre are equal.

5. An arc of a circle is intercepted by an angle if
(a) the end-points of the arc lie on the arms of the angle and
(b) each arm of the angle contains at least one end-point.

6. An angle ‘Nith its vertex at the centre of a circle is called a central angle of the circle.

7. In a circle, if two central angles are equal, then the intercepted arcs are congruent.

8. In a circle, with centre 0
(i) degree measure of minor MN is the measure of the central angle MON, that is, m (minor MN) = LMON,
(ii) degree measure of major MN is 360° - m (minor MN) and (iii) degree measure of a semi-circle is 180°.

9. Degree measure of a whole circle is 360°.

10. To each ∠AOB, there exists at 0, another angle called, reflex ∠AOB such that reflex ∠ADB = 360°.

11. An angle is said to be inscribed in a circle if
(i) its vertex lies on the circle and (ii) each of its arms intersects the circle in two distinct points.

12. In a circle, the measure of an inscribed angle is half the measure of its intercepted arc.

13. The angle an arc subtends at the centre is twice the angle it subtends at any point on the remaining part of the circle.

14. Two angles are said to be inscribed in the same arc (or the same segment) of a circle, if they intercept the same arc.

15. Angles inscribed in the same arc of a circle are equal.

16. Angle in a semicircle is a right angle.

17. A quadrilateral is said to be a cyclic quadrilateral, if its vertices lie on a circle.

18. Opposite angles of a cyclic quadrilateral are supplementary.

19. A secant line of a circle is a line that intersects the circle at two distinct points.

20. A tangent line to a circle is a line in its plane that intersects the circle at exactly one point.

21. The point common to a circle and its tangent is called the point of contact. In a circle, the tangent at a point and the radius through the point of contact are perpendicular to each

22. In a circle, the tangent at a point and the radius throuygh the poijnt of contact are perpendicualr to each other.

23. A line through the end point of a radius of a circle, perpendicular to the radius, is tangent to the circle at the point.

24. At each point of a cirlce, there is one and only one tangent to the circle.

25. If the line PA is tangent to a cirlce, at the point A on it, then the line segment PA is called the tangent segment from P to the circle.

26. The length of the tangent segment from a point P to a circle, is called the length of the tangent from P to the circle.

27. Lengths of the two tangents to a circle from an external point are equal.

28. The two tangents to a circle from an external point are equally inclined to the line joining the point to the centre of the circle.

Question. A triangle ABC is inscribed in a circle, and the bisectors of the angles meet the circumference at X, Y, Z. The angles of the triangle X, Y, Z are respectively
(A) 90º - , 90º - B/2,90º - C/2
(B) 90°, 60°, 30°
(C) A/2,B/2,C/2
(D) B/2,A/2,A/2,B/2

Answer: A

Question. The chord of the larger of two concentric circles is tangent to the smaller circle and has length ‘a’. The area enclosed between the concentric circles is
(A) πa2
(B) πa2/2
(C) πa2/4
(D) cannot be determined from given data

Answer: C

Question. A regular decagon (10 sides) is inscribed in a circle. The angle that each side of the decagon subtends at the centre is
(A) 100°
(B) 42°
(C) 36°
(D) 24°

Answer: C

Question. A circle has
(A) 10 sides
(B) 20 sides
(C) 3000 sides
(D) infinite sides

Answer: D

Question. The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to
(A) 30°
(B) 45°
(C) 60°
(D) 90°

Answer: A

Question. In the given circle ABCD, O is the centre and ∠BDC = 42°. Then ∠ACB is equal to 

(A) 42°
(B) 45°
(C) 48°
(D) 60°

Answer: C

Question. Two parallel chords on the same side of the centre of a circle are 10 cm and 24 cm long and their distance apart is 7 cm. The radius of the circle is
(A) 13 cm
(B) 8 cm
(C) 5 cm
(D) 7 cm

Answer: A

Question. Two chords of a circle bisect each other. Then thye must be
(A) diameters
(B) tangents
(C) secants parallel to each other
(D) none of the foregoing

Answer: A

Question. A telegraph wire spans 20 m with a dip at the centre of 10 cm. Assuming the wire is in the form of a circular arc, its radius is
(A) 45 m
(B) 116 m
(C) 208 m
(D) 500.05 cm

Answer: D

Question. AB is a chord of a circle of radius 4.3 cm and P is a point on it which divides it into two parts in the ratio 7 : 10. If P is 2.7 cm distance from the centre O, the length of AB is
(A) 5 cm
(B) 6.8 cm
(C) 6.4 cm
(D) 6.1 cm

Answer: B

Question. A circle with radius 2 units is intersected by a line at points R and T. The maximum possible distance between R and T is
(A) 1 unit
(B) 2π units
(C) 4π units
(D) 4 units

Answer: D

Question. P, Q, R, S, T and U are points on the circle shown below and the length of arc PQR is 6 cm. Then length of arc STU is 

(A) 12 cm
(B) 6π cm
(C) 6 cm
(D) cannot be determined from the given data

Answer: D

Question. O is the centre of the circle as shown in the diagram. The distance between P and Q is 4 cm. Then the measure of ∠ROQ is 

(A) y°
(B) 35°
(C) 105°
(D) 70°

Answer: D

Question. RS is a diameter of circle as shown in the diagram. X is a point lying outside the circle. Then ∠RXS is 

(A) 90°
(B) greater than 90°
(C) lesser than 90°
(D) cannot be determined from given data

Answer: C

Question. C is the centre of the circle as shown in the diagram below. Then x + y is equal to 

(A) 90°
(B) 100°
(C) 130°
(D) 45°

Answer: A

Question. E and F are two points on a circle O. Point G is inside circle O and point H is outside circle O. The degree measure of ∠EHF is 
(A) 60°
(B) greater than 60°
(C) less than 60°
(D) cannot be determined from given data

Answer: D

Question. Given a circle as shown in figure below. If the length of arc ABC is 12 cm then length of arc ADC is 

(A) 12 cm
(B) 8 cm
(C) 16 cm
(D) cannot be determined from given data

Answer: D

Question. Triangle PQR is inscribed in a circle. If PQ= 4 m then QR is equal to 

(A) 4 cm
(B) 8 cm
(C) 6 cm
(D) cannot be determined from given data

Answer: A

Question. In the figure given below O is the centre of the circle. Line AB intersects the circle only at point B, and line DC intersects the circle only at point C. If th e circle has a radius of 2 cm, then AC is 

(A) 4 cm
(B) 2 + √2 cm
(C) 4 + √2 cm
(D) 2 + 2 √2 cm

Answer: D

Question. The length l of a tanget, drawn from a point A to a circle is 4/3 of the radius r. The shortest distance from A to the circle is 
(A) 1/2 r
(B) r
(C) 1/2 l
(D) 2/3 l

Answer: C

Question. The radius of a circle is 2.5 cm. AB and CD are two parallel chores 2.7 m apart. If AB = 4.8 cm then CD is equal to
(A) 4.8 cm
(B) 2.4 cm
(C) 3 cm
(D) 4 cm

Answer: C

Question. The diameter is
(A) smallest chord of a circle
(B) greatest chord of a circle
(C) three times radius of circle
(D) none of the foregoing

Answer: B

Question. Given a circle and a quadrilateral ABCD inscribed in it as shown. 

If ∠B = 125°, ∠E is equal to
(A) 55°
(B) 125°
(C) 130°
(D) 62.5°

Answer: A

Question. Given a chord AB in a circle as shown. If two more chords AD and BE are drawn perpendicular to AB then 

(A) AD = BE
(B) AD = 2BE
(C) 2AD = BE
(D) none of these

Answer: A

Question. PQ, PR are tangents to a circle and QS is a diameter. Then 
(A) ∠QPR = 1/2 ∠RQS
(B) ∠QPR = 2∠RQS
(C) ∠QPR = ∠RQS
(D) none of the foregoing

Answer: B

Question. ABCD is a cyclic quadrilateral. If ∠ACB = ∠ADB then
(A) ABCD is a cyclic quadrilateral
(B) ABCD is a parallelogram
(C) ABCD is a square
(D) ABCD is not a cyclic quadrilateral

Answer: A

Question. As shown in figure, ABC is a triangle inscribed in a circle with centre O. If ∠OBC = 30° then ∠A is equal to 

(A) 30°
(B) 60°
(C) 45°
(D) 75°

Answer: B

Question. Which of the following is a cyclic quadrilateral?
(A) Trapezium
(B) Parallelogram
(C) Rhombus
(D) Rectangle

Answer: D

Question. O is the centre of a circle and if ∠A + ∠BOC = 120° then ∠BOC is equal to

(A) 80°
(B) 30°
(C) 60°
(D) 100°

Answer: A

Question. A̅B̅,C̅D̅,E̅F̅ and G̅H̅ are chords of a circle. If A̅B̅ = 3.5 cm, CD = 4 cm, EF = 3 cm and GH = 5 cm then the chord nearest to the centre of he circle is
(A) A̅B̅
(B) C̅D̅
(C) E̅F̅
(D) G̅H̅

Answer: D

Question. The circumference of a circle is 60 cm. The length of an arc of 90° is
(A) 10 cm
(B) 15 cm
(C) 20 cm
(D) None

Answer: B

Question. A circle is divided into 12 equal parts. The number of degrees in each arc is
(A) 30°
(B) 60°
(C) 45°
(D) None

Answer: A

Question. An equilateral triangle XYZ is inscribed in a circle with centre O. The measure of XOY is
(A) 60°
(B) 120°
(C) 45°
(D) 75°

Answer: B

Question. A diameter of a circle is also a
(A) tangent
(B) chord
(C) secant
(D) radius

Answer: B

Question. The number of tangents that can be drawn to a circle at a given point on it is
(A) two
(B) one
(C) zero
(D) three

Answer: D

Question. In a circle, the major arc is twice the minor arc. The corresponding central angles and the degree measures of the two arcs are
(A) 90° and 270°
(B) 60° and 300°
(C) 240° and 120°
(D) 120° and 240°

Answer: C

Question. AB, BC and CD are equal chords of a circle with O as the centre. ∠AOB is
(A) 60°
(B) 120°
(C) 90°
(D) not necessarily any of the foregoing

Answer: D

Question. One side of a regular polygon with vertices on a circle subtends an angle of 20° at the centre of this circle. This polygon is
(A) 20-sided
(B) 18-sided
(C) 9-sided
(D) 6-sided

Answer: B

Question. In the figure drawn below if ∠C = 30° , then ∠A and ∠B are respectively 

(A) 60° and 90°
(B) 90° and 60°
(C) 45° and 105°
(D) 75° and 75°

Answer: A

Question. The least number of noncollinear points required to draw a circle passing through them is
(A) two
(B) three
(C) four
(D) nine

Answer: B

1. A circle is closed curve in a plane drawn in such a way that every point on this curve is at a constant distance (r units) from a fixed point O inside it.
The fixed point O is called the centre of the circle and the constant distance r is called the length of radius of the circle.

2. Circumference of a circle: The perimeter of a circle is called its circumference. The length of the thread that winds tightly around the circle exactly once given the circumference of the circle.
Circumference = 2πr = pπ, where r = radius and d = diameter.
Here π(Pi) is a constant.
Note : The approximate value of π is taken as 22/7 or 3.14. However π is not a rational number. It is an irrational number and is defined as the ratio of circumference of a circle to its diameter.

3. Area of a circle : Area of a circle with radius r units is equal to πr² sq units.

4. Area of a ring : The region enclosed between two concentric circles of different radii is called a ring. 

Area of path formed = (πR² – πr²) sq units
= π(R² – r²) sq units
= π(R + r) (R – r) sq units

5. Length of Arc of a circle : Let A and B be any two points on a circle. The length of the thread that will wrap along this arc from A to B is the length of AB written as A̅B̅ . 

6. Area of a sector : A sector of a circle is the region enclosed by an arc of a circle and two radii to its end points.

Area of sector = xº/360º x πr² where x is sector angle and r is radius of circle. 

7. Segment of a circle : A segment of a circle is the region enclosed by an arc of the circle and its chord.
Area of minor segment A X B = area of sector OA X B – area of ΔOAB 

Area of major segment A Y B = area of circle – area of minor segment A X B

Question. If the ratio of areas of two circles is 16 : 25 the ratio of their circumference is
(A) 25 : 16
(B) 5 : 4
(C) 4 : 5
(D) 3 : 5

Answer: C

Question. If the ratio of circumference of two circles is 4 : 9, the ratio of their area is
(A) 9 : 4
(B) 16 : 81
(C) 4 : 9
(D) 2 : 3

Answer: B

Question. If the area of a circle is A, radius of the circle is r and circumference of it is C, then
(A) rC = 2A
(B) C/A = r/2
(C) AC = r²/4
(D) A/r = C

Answer: A

Question. The area of a sector of a circle of radius 16 cm cut of by an arc which is 18.5 cm long is
(A) 168 cm²
(B) 148 cm²
(C) 154 cm²
(D) 176 cm²

Answer: B

Question. The area of a segment of a circle of radius 21 cm if the arc of the segment has a measure of 60° is (Tank √3 =1.73)
(A) 45.27 cm²
(B) 40.27 cm²
(C) 40.8 cm²
(D) None

Answer: B

Question. If the radii of two concentric circles are 15 cm and 13 cm respectively, then the area of the circulating ring in sq cm will be
(A) 176
(B) 178
(C) 180
(D) 200

Answer: A

Question. The area of the largest triangle that can be inscribed in a semicircle whose radius is r cm is
(A) 2r cm²
(B) r² cm²
(C) 2r² cm²
(D) r/2 cm²

Answer: B

Question. A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is given by
(A) 11 : 12
(B) 21 : 33
(C) 22 : 33
(D) 14 : 11

Answer: D

Question. The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. The radius of cone of the three concentric circles is
(A) 8 √3 cm
(B) 2 √3 cm
(C) 10 √3 cm
(D) 14 √3 cm

Answer: C

Question. A sector of 120° cut out from a circle has an area of 9,3/7 sq cm. The radius of the circle is
(A) 3 cm
(B) 2.5 cm
(C) 3.5 cm
(D) 3.6 cm

Answer: A

Question. The radius of a circle is 14 m, then the circumference of a circle is
(A) 616 m
(B) 88 m
(C) 154 m
(D) None

Answer: B

Question. The circumference of a circle is 44 m, then the area of the circle is
(A) 6084.5 m²
(B) 276.5 m²
(C) 154 m²
(D) 44 m²

Answer: C

Question. The area of a circle is 2464 m², then the diameter is
(A) 56 m
(B) 154 m
(C) 176 m
(D) None

Answer: A

Question. A circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside. The are of the path is
(A) 1496 m²
(B) 1450 m²
(C) 1576 m²
(D) 1694 m²

Answer: D

Question. The difference between circumference and radius of a circle is 37 m. The circumference of that circle is
(A) 7 m
(B) 44 m
(C) 154 m
(D) None

Answer: B

Question. The area of the sector of a circle, whose radius is 6 m when the angle at the centre is 42° is
(A) 13.2 m²
(B) 14.2 m²
(C) 13.4 m²
(D) 14.4 m²

Answer: B

Question. If the radius of a circle is 7√π cm, then the area of the circle is
(A) 154 cm²
(B) 49 /π
(C) 22 cm²
(D) 49 cm²

Answer: D

Question. If the circumference of a circle is 30/π , then the diameter of the circle is
(A) 60 π
(B) 15/π
(C) 30/π²
(D) 30

Answer: C

Question. How many plants will be there in a circular bed whose outer edge measures 30 cm allowing 4 cm² for each plants?
(A) 18
(B) 750
(C) 24
(D) 120

Answer: A

Question. When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to
(A) area
(B) circumference
(C) 2 π
(D) 4

Answer: D