Mathematics Class IX

Question 1 of 50

1. Question
1 point(s)
In the following figure, O is the centre of the circle and the points P, Q and R lie on it. If the angle POR is 96°, then what is the angle QPR?
- 48°
- 64°
- 36°
- 72°
Correct

Incorrect

Hint

The angle subtended on any part of the circle is half the angle subtended at the centre of the circle.

(1) $\begin{equation*}\begin{split} \angle QPR &= \dfrac{96^{\circ}}{2} \\ &= 48^{\circ} \end{split}\end{equation*}$
Question 2 of 50

2. Question
1 point(s)
In the following figure, O is the centre of the circle and the points E, F and G lie on it. If the angles GOE and OFE are 100° and 16° respectively, then what is the angle GFO?
- 50°
- 34°
- 44°
- 38°
Correct

Incorrect

Hint

The angle subtended on any part of the circle is half the angle subtended at the centre of the circle.

(1) $\begin{equation*}\begin{split} \angle GFE &= \dfrac{100^{\circ}}{2} \\ &= 50^{\circ} \\ \angle GFO + 16^{\circ} &= 50^{\circ} \\ \angle GFO &= 34^{\circ} \end{split}\end{equation*}$
Question 3 of 50

3. Question
1 point(s)
In the following figure, O is the centre of the circle and the points E, F and G lie on it. If the angle GFE is 83°, then what is the reflex angle GOE?
- 186°
- 204°
- 194°
- 166°
Correct

Incorrect

Hint

The angle subtended on the centre of the circle is double the angle subtended at any point on the circle.

(1) $\begin{equation*}\begin{split} \angle GOE &= 2 \times 83^{\circ} \\ &= 166^{\circ} \\ reflex \angle GOE &= 360^{\circ} - 166^{\circ} \\ &= 194^{\circ} \end{split}\end{equation*}$
Question 4 of 50

4. Question
1 point(s)
In the following figure, points P, Q, R and S lie on a circle. If the angle PQS is 67°, then what is the angle PRS?
- 73°
- 43°
- 57°
- 67°
Correct

Incorrect

Hint

Angles drawn in the same segment of a circle are equal in measure. $\angle PRS &= 67^{\circ}$
Question 5 of 50

5. Question
1 point(s)
In the following figure, points A, B, C and D lie on a circle. If the angles ABD and CAD are 43° and 65°, then what is the angle CDA?
- 64°
- 72°
- 43°
- 82°
Correct

Incorrect

Hint

Angles drawn in the same segment of a circle are equal in measure. $\angle ACD &= 43^{\circ}$ Sum of all angles of a triangle is 180°.

(1) $\begin{equation*}\begin{split} \angle CDA + 43^{\circ} + 65^{\circ} &= 180^{\circ} \\ \angle CDA &= 72^{\circ} \end{split}\end{equation*}$
Question 6 of 50

6. Question
1 point(s)
In the following figure, points E, F, G and H lie on a circle. P is the point of intersection of the lines FH and GE. If the angles EFH and GPH are 41° and 93°, then what is the angle GHP?
- 61°
- 41°
- 54°
- 46°
Correct

Incorrect

Hint

Angles drawn in the same segment of a circle are equal in measure. $\angle EGH &= 41^{\circ}$ Sum of all angles of a triangle is 180°.

(1) $\begin{equation*}\begin{split} \angle GHP + 41^{\circ} + 93^{\circ} &= 180^{\circ} \\ \angle GHP &= 46^{\circ} \end{split}\end{equation*}$
Question 7 of 50

7. Question
1 point(s)
PQRS is a cyclic quadrilateral. If the angle QPS are is 108°, then what is the angle QRS?
- 72°
- 108°
- 54°
- None of these
Correct

Incorrect

Hint

Sum of opposite angles of a cyclic quadrilateral is 180°.

(1) $\begin{equation*}\begin{split} \angle QRS + 108^{\circ} &= 180^{\circ} \\ \angle QRS &= 72^{\circ} \end{split}\end{equation*}$
Question 8 of 50

8. Question
1 point(s)
ABCD is a cyclic quadrilateral. Triangle ADC is an isosceles triangle with AD = CD. If the angle ABC are is 96°, then what is the angle ACD?
- 42°
- 54°
- 48°
- 64°
Correct

Incorrect

Hint

Sum of opposite angles of a cyclic quadrilateral is 180°.

(1) $\begin{equation*}\begin{split} \angle ADC + 96^{\circ} &= 180^{\circ} \\ \angle ADC &= 84^{\circ} \end{split}\end{equation*}$

Angles opposite to equal sides are equal and sum of all three angles of a triangle is 180°.

(2) $\begin{equation*}\begin{split} \angle ACD + \angle CAD + 84^{\circ} &= 180^{\circ} \\ \angle ACD + \angle ACD &= 96^{\circ} \\ \angle ACD &= 48^{\circ} \end{split}\end{equation*}$
Question 9 of 50

9. Question
1 point(s)
EFGH is a cyclic quadrilateral. What is the value of k?
- 22°
- 24°
- 27°
- 29°
Correct

Incorrect

Hint

Sum of opposite angles of a cyclic quadrilateral is 180°.

(1) $\begin{equation*}\begin{split} 5k-23 + 3k+27 &= 180^{\circ} \\ 8k+4 &= 180^{\circ} \\ 8k &= 176^{\circ} \\ k &= 22^{\circ} \end{split}\end{equation*}$
Question 10 of 50

10. Question
1 point(s)
In the following figure, points A, B and C lie on a circle and O is the centre of the circle. If the angle ABC is 47°, then what is the angle ACB?
- 43°
- 37°
- 47°
- 33°
Correct

Incorrect

Hint

Angles drawn in a semicircle is a right angle. $\angle BAC &= 90^{\circ}$ Sum of all angles of a triangle is 180°.

(1) $\begin{equation*}\begin{split} \angle ACB + 90^{\circ} + 47^{\circ} &= 180^{\circ} \\ \angle ACB &= 43^{\circ} \end{split}\end{equation*}$
Question 11 of 50

11. Question
1 point(s)
In the following figure, points P, Q, R and S lie on a circle and O is the centre of the circle. If the angles QPR and and PRS are 52° and 62° respectively, then what is the angle QPS?
- 90°
- 80°
- 85°
- 95°
Correct

Incorrect

Hint

Angles drawn in a semicircle is a right angle. $\angle PSR &= 90^{\circ}$ Sum of all angles of a triangle is 180°.

(1) $\begin{equation*}\begin{split} \angle SPR + 90^{\circ} + 62^{\circ} &= 180^{\circ} \\ \angle SPR &= 28^{\circ} \\ \angle QPS &= 52^{\circ} + 28^{\circ} \\ \angle QPS &= 80^{\circ} \end{split}\end{equation*}$
Question 12 of 50

12. Question
1 point(s)
In the following figure, points P, Q, R and S lie on a circle and O is the centre of the circle. If the angle QRS is 126° respectively, then what is the angle QSP?
- 44°
- 36°
- 54°
- 27°
Correct

Incorrect

Hint

Angles drawn in a semicircle is a right angle. $\angle PQS &= 90^{\circ}$ Sum of opposite angles of a quadrilateral is 180°.

(1) $\begin{equation*}\begin{split} \angle QPS + 126^{\circ} &= 180^{\circ} \\ \angle QPS &= 54^{\circ} \end{split}\end{equation*}$

Sum of all angles of a triangle is 180°.

(2) $\begin{equation*}\begin{split} \angle QSP + 90^{\circ} + 54^{\circ} &= 180^{\circ} \\ \angle QSP &= 36^{\circ} \end{split}\end{equation*}$
Question 13 of 50

13. Question
1 point(s)
In the following figure, AB is a chord of the circle and O is the centre of the circle. Also OC is perpendicular bisector of AB. If OC = 8 cm and AB = 30 cm respectively, then what is the radius of the circle?
- 23 cm
- 15 cm
- 17 cm
- 21 cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} AC &= 15 \\ OA^{2} &= AC^{2} + OC^{2} \\ OA^{2} &= 15^{2} + 8^{2} \\ OA^{2} &= 225+64 \\ OA^{2} &= 289 \\ OA &= 17 \end{split}\end{equation*}$

Radius of the circle is 17 cm.
Question 14 of 50

14. Question
1 point(s)
In the following figure, AB is a chord of the circle and O is the centre of the circle. Also OC is perpendicular bisector of AB. If OC = 20 cm and OA = 29 cm respectively, then what is the length of the chord AB?
- 44 cm
- 38 cm
- 42 cm
- 40 cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} OA^{2} &= AC^{2} + OC^{2} \\ 29^{2} &= AC^{2} + 20^{2} \\ 841 &= AC^{2}+400 \\ 441 &= AC^{2} \\ 21 &= AC \end{split}\end{equation*}$

Length of the chord AB is 42 cm.
Question 15 of 50

15. Question
1 point(s)
In the following figure, AB is a chord of the circle and O is the centre of the circle. Also OC is perpendicular bisector of AB. If the radius of the circle is 10 cm and the length of the chord AB is 16 cm, then what is the length of OC?
- 5 cm
- 7 cm
- 8 cm
- 6 cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} AC &= 8 \\ OA^{2} &= AC^{2} + OC^{2} \\ 10^{2} &= 8^{2} + OC^{2} \\ 100 &= 64+OC^{2} \\ 36 &= OC^{2} \\ 6 &= OC \end{split}\end{equation*}$
Question 16 of 50

16. Question
1 point(s)
In the following figure, AB and CD are chords of a circle. AB = 18 cm, PO = 12 cm and OQ = 9 cm, then what is the length of CD?
- 30 cm
- 16 cm
- 12 cm
- 24 cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} PB &= 9 \\ OB^{2} &= PO^{2} + PB^{2} \\ OB^{2} &= 12^{2} + 9^{2} \\ OB^{2} &= 225 \\ OB &= 15 \\ OB &= OD \\ OD^{2} &= OQ^{2}+QD^{2} \\ 15^{2} &= 9^{2}+QD^{2} \\ 225 &= 81+QD^{2} \\ 144 &= QD^{2} \\ 12 &= QD \\ CD &= 24 \end{split}\end{equation*}$
Question 17 of 50

17. Question
1 point(s)
In the following figure, AB and CD are chords of a circle. The chords AB and CD are at equal distance from the centre O. If the length of chord AB is 16 cm then what is the length of the chord CD?
- 16 cm
- 12 cm
- 8 cm
- 20 cm
Correct

Incorrect

Hint

The chords which are at equal distance from the centre are equal in length. Therefore, CD is also 16 cm long.
Question 18 of 50

18. Question
1 point(s)
In the following figure, AB and CD are chords of a circle. The chords AB and CD are equal in length. If the chord AB is at 12 cm from the centre of the circle then what is the length of OT?
- 8 cm
- 16 cm
- 12 cm
- 6 cm
Correct

Incorrect

Hint

Equal chords are at equal distance from the centre. Therefore, OT is also 12 cm long.
Question 19 of 50

19. Question
1 point(s)
In the following figure, two circles are concentric. OC is the perpendicular bisector of AB. If the radius of the small circle is 8 cm and the radius of the big circle is 17 cm, then what is the length of the chord AB?
- 15 cm
- 30 cm
- 25 cm
- 20 cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} OC^{2} + CB^{2} &= OB^{2} \\ 8^{2}+CB^{2} &= 17^{2} \\ CB^{2} &= 225 \\ CB &= 15 \\ AB &= 30 \end{split}\end{equation*}$
Question 20 of 50

20. Question
1 point(s)
In the following figure, two circles are concentric. OC is the perpendicular bisector of AB. If the radius of the small circle is 20 cm and the length of the chord AB is 42 cm, then what is the radius of the small circle?
- 31 cm
- 27 cm
- 32 cm
- 29 cm
Correct

Incorrect

Hint

(1) $\begin{equation*}\begin{split} CB &= 21 \\ OC^{2} + CB^{2} &= OB^{2} \\ 20^{2}+21^{2} &= OB^{2} \\ 841 &= OB^{2} \\ 29 &= OB \end{split}\end{equation*}$
Question 21 of 50

21. Question
1 point(s)
Collection of those points in a plane that are at a given constant distance from a given fixed point in the plane is called a-
- Square
- Circle
- Quadrilateral
- Triangle
Correct

Incorrect

Hint

Collection of those points in a plane that are at a given constant distance from a given fixed point in the plane is called a circle
Question 22 of 50

22. Question
1 point(s)
Interior of the circle lies-
- Outside the circle
- Inside the circle
- On the circle
- None of the above
Correct

Incorrect

Hint

Interior of the circle lies inside the circle.
Question 23 of 50

23. Question
1 point(s)
Exterior of the circle lies-
- Outside the circle
- Inside the circle
- On the circle
- None of the above
Correct

Incorrect

Hint

Exterior of the circle lies outside the circle.
Question 24 of 50

24. Question
1 point(s)
The centre of a circle lies-
- On the circle
- Outside the circle
- Inside the circle
- None of the above
Correct

Incorrect

Hint

The centre of a circle lies inside the circle.
Question 25 of 50

25. Question
1 point(s)
A line segment joining any two points of a circle is called-
- An arc
- Chord
- Radius
- Diameter
Correct

Incorrect

Hint

A line segment joining any two points of a circle is called chord.
Question 26 of 50

26. Question
1 point(s)
A chord passing through the centre of a circle is known as-
- Diameter
- Centroid
- Concentric
- None of the above
Correct

Incorrect

Hint

A chord passing through the centre of a circle is known as diameter.
Question 27 of 50

27. Question
1 point(s)
The longest chord of a circle is called-
- Major arc
- Radius
- Diameter
- Major segment
Correct

Incorrect

Hint

The longest chord of a circle is called diameter.
Question 28 of 50

28. Question
1 point(s)
A point, whose distance from the centre of a circle is greater than its radius lies-
- Outside the circle
- Inside the circle
- On the circle
- None of the above
Correct

Incorrect

Hint

A point, whose distance from the centre of a circle is greater than its radius lies outside the circle.
Question 29 of 50

29. Question
1 point(s)
In how many parts a circle divides the plane,on which it lies?
- Three
- Two
- One
- Zero
Correct

Incorrect

Hint

A circle divides the plane,on which it lies, in three parts.
Question 30 of 50

30. Question
1 point(s)
Which of the following is true?
- A circle is a plane figure.
- Line segment joining the centre to any point on the circle is a radius of the circle.
- If a circle is divided into three equal arcs, each is a major arc.
- All of the above
Correct

Incorrect

Hint

All of the above are correct.
Question 31 of 50

31. Question
1 point(s)
Which circles are said to be concentric circles?
- Same centre and same radii
- Different centre and different radii
- Different centre and same radii
- Same centre and different radii
Correct

Incorrect

Hint

Concentric circles have same centre and different radii.
Question 32 of 50

32. Question
1 point(s)
Which of the following is NOT true?
- A circle has only finite number of equal chords.
- A chord of a circle, which is twice as long is its radius is a diameter of the circle.
- Sector is the region between the chord and its corresponding arc.
- None of the above
Correct

Incorrect

Hint

A circle has infinite number of equal chords
Question 33 of 50

33. Question
1 point(s)
The collection of points of the circle that lie on and also inside a central angle is called-
- Major arc
- Major segment
- Minor segment
- Minor arc
Correct

Incorrect

Hint

The collection of points of the circle that lie on and also inside a central angle is called a minor arc.
Question 34 of 50

34. Question
1 point(s)
Which of the following is NOT true?
- Degree measure of a semi-circle is 180°
- The degree measure of an arc is the complement of the central angle containing the arc.
- Degree measure of a semi-circle is 360°
- None of the above
Correct

Incorrect

Hint

Degree measure of a semi-circle is 180°
Question 35 of 50

35. Question
1 point(s)
The collection of points of the circle that lie on or outside a central angle is called-
- Major arc
- Major segment
- Minor segment
- Minor arc
Correct

Incorrect

Hint

The collection of points of the circle that lie on or outside a central angle is called major arc.
Question 36 of 50

36. Question
1 point(s)
Length of the fine thread which just covers the arc completely is called-
- Length of an arc
- Diameter
- Radius
- Chord
Correct

Incorrect

Hint

Length of the fine thread which just covers the arc completely is called length of an arc.
Question 37 of 50

37. Question
1 point(s)
A continuous piece of circle is called-
- Segment of a circle
- Radius of a circle
- Chord of a circle
- Arc of a circle
Correct

Incorrect

Hint

A continuous piece of circle is called arc of a circle.
Question 38 of 50

38. Question
1 point(s)
Which of the following is NOT true?
- If two circles intersect at two points, then their centres lie on the perpendicular bisector of the common chord.
- Only one circle passes through the three given non-collinear points.
- Both a and b
- Neither a nor b
Correct

Incorrect

Hint

Both a and b are correct.
Question 39 of 50

39. Question
1 point(s)
What are the properties of concentric circles?
- Radii are equal
- Equal chords of congruent circles subtend equal angles at their centres.
- They cover each other exactly.
- All of the above
Correct

Incorrect

Hint

All of the above are correct.
Question 40 of 50

40. Question
1 point(s)
How many circles can pass through given three given points?
- One
- Two
- Three
- None of the above
Correct

Incorrect

Hint

Only three circles can pass through given three given points.
Question 41 of 50

41. Question
1 point(s)
Equal chords of a circle subtends___ angle at the centre.
- Acute
- Equal
- Obtuse
- Right
Correct

Incorrect

Hint

Equal chords of a circle subtends equal angle at the centre.
Question 42 of 50

42. Question
1 point(s)
Two circles can intersect each other at how many points?
- Zero
- One
- Two
- All of the above
Correct

Incorrect

Hint

All of the above are correct.
Question 43 of 50

43. Question
1 point(s)
Equal chords of a circle are equidistant from-
- The centre
- Any exterior point
- Any interior point
- Radius of the circle
Correct

Incorrect

Hint

Equal chords of a circle are equidistant from the centre.
Question 44 of 50

44. Question
1 point(s)
Angles in the same segment of a circle are-
- Acute
- Equal
- Obtuse
- Right
Correct

Incorrect

Hint

Angles in the same segment of a circle are equal.
Question 45 of 50

45. Question
1 point(s)
Which of the following is true?
- If two arcs of a circle are congruent, then corresponding chords are equal.
- Chords of a circle which are equidistant from the centre are equal.
- If the angles subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- All of the above
Correct

Incorrect

Hint

All of the above are correct.
Question 46 of 50

46. Question
1 point(s)
Which of the following is true?
- Equal chords of a circle subtend equal angles at the centre.
- If angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
- Both a and b
- Neither a nor b
Correct

Incorrect

Hint

Both a and b are correct.
Question 47 of 50

47. Question
1 point(s)
The region between the chord and its corresponding arc is called-
- Segment
- Sector
- Region
- Common area
Correct

Incorrect

Hint

The region between the chord and its corresponding arc is called sector.
Question 48 of 50

48. Question
1 point(s)
Which of the following is NOT true?
- The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
- The perpendicular from the centre of a circle to a chord bisects the chord.
- Both a and b
- Neither a nor b
Correct

Incorrect

Hint

Both a and b are correct.
Question 49 of 50

49. Question
1 point(s)
An arc is a ___ when its ends are the ends of a diameter.
- Segment
- Semi-circle
- Diameter
- Chord
Correct

Incorrect

Hint

An arc is a semi-circle when its ends are the ends of a diameter.
Question 50 of 50

50. Question
1 point(s)
Angles with end points of a diameter of a circle are-
- Right angles
- Acute angles
- Obtuse angles
- Straight angles
Correct

Incorrect

Hint

Angles with end points of a diameter of a circle are right angles.