Class 9 Practice – Level 1 – Circles Leave a Comment / By Gulam Hamza / September 12, 2024 Class 9 Practice – Level 1 – Circles Total questions: 40 1. In the given figure two circles are congruent if they have the same radii. select the correct option? Topic: Congruence of Circles ∠AOB = ∠CO′D ∠ABO = ∠CO′D ∠AOB = ∠OC′D None of these None 2. If chords of congruent circles subtend equal angles at their centres, then the chords are equal. Topic: Chords and Angles in Congruent Circles True False None 3. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord. Topic: Common Chord Length 3cm 6cm 8cm None of these None 4. If two equal chords of a circle intersect within the circle, within the circle in the given figure, which of the following option is true ? Topic: Intersecting Chords EA = EC and AE = EA EB = EC and AE = ED ED = EC and AE = PD None of these None 5. If two equal chords of a circle intersect within the circle, which option is correct in the given figure? Topic: Intersecting Chords ∠OXA= ∠OXD ∠OXA = ∠CXD ∠ONA = ∠OXD None of these None 6. If a line intersects two concentric circles (circles with the same centre) with centre O at A,B,C and D, select the correct option? Topic: Concentric Circles AD=BC CB=AC AB=CD All of these None 7. In the figure A,B and C are three points on a circle with centre O such that ∠BOC=30° and ∠AOB=60°. If D is a point on the circle other than the arc ABC, find ∠ADC. Topic: Angles in a Circle 45° 90° 35° 65° None 8. 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. Topic: Angle Subtended by a Chord 200°, 60° 250° , 40° 150° , 30° None of these None 9. In the figure, angle PQR=100°, where P,Q and R are points on a circle with centre O. Find angle OPR. Topic: Angles in a Cyclic Quadrilateral 10° 20° 30° 40° None 10. In the figure, ∠ABC=69°, ∠ACB=31°, find ∠ADC. Topic: Angles in a Circle 50° 60° 100° 111° None 11. In the given figure, A,B,C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC=130° and ∠ECD=20°. Find ∠BAC. Topic: Intersecting Chords and Angles 50° 90° 110° 65° None 12. In the given figure, AB is parallel to DC,∠BCE=80° and ∠BAC=25° . Find ∠CAD Topic: Parallel Chords and Angles 55° 65° 25° 75° None 13. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ΔDBC=70°, ΔBAC is 30°, find ∠ BCD. Further if AB=BC, find ∠ ECD. Topic: Cyclic Quadrilateral Angles ∠ BCD = 80°, ∠ ECD = 50° ∠ BCD = 90°, ∠ ECD = 60° ∠ BCD = 50°, ∠ ECD = 70° ∠ BCD = 75°, ∠ ECD = 75° None 14. If the non-parallel sides of a trapezium are equal, what is ∠A + ∠C. Topic: Angles in an Isosceles Trapezium 180° 90° 60° 40° None 15. Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A,D and P,Q respectively (see figure) and select the correct option? Topic: Intersecting Chords and Angles ∠AQP = ∠QCD ∠ACP = ∠QCD ∠ADP = ∠QCP None of these None 16. If circles are drawn taking two sides of a triangle as diameters, select the correct option? Topic: Circles on Triangle's Sides as Diameters C lies on the BC. D lies on the BC. D lies on the AC. None of above None 17. ABC and ADC are two right triangles with common hypotenuse AC. select the correct answer? Topic: Right Triangles with Common Hypotenuse ∠CBD=∠CAD ∠CAD=∠CBD ∠ACD=∠CBD None of the above None 18. ABCD is a cyclic parallelogram which is the following statement is correct? Topic: Cyclic Parallelogram Properties ABCD is a triangle ABCD is a Circle. ABCD is a rectangle. None of these None 19. In the given figure the line of centres of two intersecting circles subtends equal angles at the two points of intersection, choose the correct option? Topic: Line of Centres and Intersection Angles ∠ADB=∠ACB ∠ACB=∠ADB ∠ABD=∠ADB None of these None 20. In the figure, ∠ABC=69°, ∠ACB=31°, find ∠BDC. Topic: Angles in a Cyclic Quadrilateral 60° 70° 80° 50° None 21. Two chords A B and C D of lengths 5 cm and 11 ~cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between A B and C D is 6 , find the radius of the circle. Topic: Parallel Chords and Radius 5.6 cm 8.6 cm 6.6 cm 5.8 cm None 22. The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre? Topic: Parallel Chords and Radius 10 cm 8 cm 6 cm 3 cm None 23. If the circle drawn with any side of a rhombus as diameter, passes through the, point of intersection of its diagonals. Topic: Circle and Rhombus Properties True False None 24. ABCD is a parallelogram. The circle through A,B and C intersect CD (produced if necessary) at E, select the correct option? Topic: Circle and Parallelogram Properties AC=DE AD=DE AB=DE None of these None 25. A C and B D are chords of a circle which bisect each other. find the value of ∠A ? Topic: Perpendicular Chords and Angles 90° 50° 60° 80° None 26. If a line intersects two concentric circles (circles with the same centre) with centre O at A,B,C and D, choose the correct option ? Topic: Concentric Circles BO = CD BC = AD AB = CD None of these None 27. In the figure, O is the centre of the circle. If ∠BOD=160°, find the values of x and y. Topic: Central Angle and Arcs x = 120°, y = 140 x = 80, y = 100° x = 40°, y = 80° None of these None 28. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, what is the value of each internal angle? Topic: Cyclic Quadrilateral Angles 60° 40° 90° 50° None 29. In the given figure, the straight lines AB and CD pass through the centre O of the circle. If ∠AOD=75 ∘ and ∠OCE=40 ∘ , Then (i) ∠CDE (ii) ∠OBE are respectively Topic: Angles in a Circle 75° and 55° 50° and 25° 40° and 55° 45° and 75° None 30. In the adjoining figure, two circles with centres A and B, and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ. Topic: Internal Tangents and Circle Properties $\displaystyle 6\sqrt{6}cm$ $\displaystyle 4\sqrt{6}cm$ $\displaystyle 4\sqrt{8}cm$ $\displaystyle 4\sqrt{4}cm$ None 31. Given an arc of a circle, complete the circle. Topic: Central Angle and Arcs Taking the centre and the Diameter so obtained Taking the centre and the radius so obtained, Taking the mid-point and the radius so obtained, None of these None 32. In the given figure, ∠ABD=54° and ∠BCD=36°, calculate ∠ACD. Topic: Angles in a Circle 45° 65° 54° 47° None 33. O is the centre of the circle, If chord AD= chord CD, then x = ? Topic: Equal Chords and Angles 70° 50° 35° 45° None 34. In the adjoining figure, DE is a chord parallel to diameter AC of the circle with centre O. If ∠CBD=60°,calculate ∠CDE. Topic: Parallel Chords and Angles 70° 40° 30° 25° None 35. In the adjoining figure, AB and AC are two equal chords of a circle with centre O, which of the following option is correct? Topic: Equal Chords in a Circle ∠OAB = ∠OAC ∠OCB = ∠OCA ∠OAC = ∠OAB None of these None 36. If a diameter of a circle bisects each of the two chords of a circle then which is the following answer is correct ? Topic: Diameter and Bisected Chords AB∥CA AB∥CD AB∥CB All of these None 37. Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B, select the correct option? Topic: Intersecting Circles and Chords QA=AB QB=AQ QB=AD None of these None 38. In the adjoining figure BC is a diameter of a circle with centre O. If AB and CD are two chords such that AB∥CD, select the correct option? Topic: Parallel Chords and Diameter AB = CD OD = BD OM = CL None of these None 39. The two different circles cannot intersect each other at more than two points ? Topic: Intersection of Two Circles True False None 40. If the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it. then which of the following statement is correct? Topic: Perpendicular Diameter and Parallel Chords NC=ND ON=AD CB=NN All of these None 1 out of 40 Time's up
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