Class 9 Practice – Level 3 – Set 1 – Circles

Total questions: 15

Two congurent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P,Q lie on the two circles. Which of the option a correct?

Topic: Intersecting Circles and Chords

∠QPB=∠PBQ

∠QPB=∠PQB

∠QPC=∠PQB

None of these

None

In any triangle ABC, if the angle bisector ∠A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

Topic: Angle Bisector and Perpendicular Bisector

BE is the right angled bisector of DC.

DE is the right angled bisector of BC.

DE is the right angled bisector of BA.

DA is the right angled bisector of BC.

None

In the given figure, O is the centre of the given circle, and chords AB and CD intersect at a point E inside the circle. If $\displaystyle \angle AOC+\angle BOD=x\times \angle AEC$, then the value of $\displaystyle x$ is ?

Topic: Intersecting Chords and Angles

None

In the given figure, O is the centre of the circle ∠OAB=30° and ∠OCB=40°. Calculate ∠AOC

Topic: Central Angles

140°

120°

130°

100°

None

In the given figure, O is the centre of the circle and ∠AOB=110°. Calculate ∠ACO and ∠CAO.

Topic: Angle at the Centre

55° ,55°

130° ,55°

255° ,35°

105° ,125°

None

In the given figure, O is the centre of the circle and ΔABC is equilateral. Find ∠BDC and ∠BEC

Topic: Angles in an Equilateral Triangle and Circle

∠BDC = 140°, ∠BEC=140°

∠BDC = 160°, ∠BEC=130°

∠BDC = 120°, ∠BEC=120°

∠BDC = 60°, ∠BEC=120°

None

In the given figure, AB is a diameter of a circle with the centre O and chord ED is parallel to AB and ∠EAB=65°. Find (i) ∠EBA (ii) ∠BED (iii) ∠BCD.

Topic: Parallel Chords and Angles

(i) 189° (ii) 85° (iii) 65°

(i) 153° (ii) 95° (iii) 25°

(i) 25° (ii) 25° (iii) 155°

(i) 125° (ii) 25° (iii) 35°

None

In the given figure, O is the centre of the circle. If ∠AOD=140 ∘ and ∠CAB=50°. Find, (i) ∠EDB (ii) ∠EBD:

Topic: Angles in a Circle

70° and 80°

50° and 110°

70° and 70°

110° and 50°

None

There are two concentric circles with the radius 17 cm and 10 cm respectively. A straight line PQRS intersects the larger circle at P and S and the smaller circle R and Q. If QR=12 cm, then the length of PS is:

Topic: Concentric Circles

15/2

None

10.

In the given figure, ABCD is a cyclic quadrilateral in which ∠CAD=25°,∠ABC= 50° and ∠ACB=35°. Then: (i) ∠CBD (ii) ∠DAB (iii) ∠ADB are respectively?

Topic: Angles in a Cyclic Quadrilateral

(i) ∠CBD=105° (ii) ∠DAB=100° (iii) ∠ADB=455°

(i) ∠CBD=65° (ii) ∠DAB=90° (iii) ∠ADB=85°

(i) ∠CBD=25° (ii) ∠DAB=70° (iii) ∠ADB=35°

(i) ∠CBD=38° (ii) ∠DAB=90° (iii) ∠ADB=85°

None

11.

In the given figure, AB is a diameter of a circle with centre O. If ADE and CBE are straight lines, meeting a E such that ∠BAD=35° and ∠BED=25°, find (i) ∠DCB (ii) ∠DBC (iii) ∠BDC.

Topic: Angles in a Circle

36°, 16° and 60°

37°, 65° and 37°

25°, 55° and 30°

35°, 115° and 30°

None

12.

In the given figure, find whether the points A, B, C, D are concyclic, when (i) 𝑥 = 70 (ii) 𝑥 = 80.

Topic: Cyclic Quadrilateral Angles

(i)No (ii)Yes

(i)Yes (ii)No

(i)No (ii)No

(i)Yes (ii)Yes

None

13.

In the given figure, the two circles intersect at P and Q. If ∠A=80° and ∠D=84° calculate : (i) ∠QBC, (ii) ∠BCP are:

Topic: Intersection of Two Circles

(i) ∠QPC=106° , (ii) ∠BCP=10°

(i) ∠QBC=100° , (ii) ∠BCP=96°

(i) ∠QBC=156° , (ii) ∠BCP=105°

(i) ∠QBC=96° , (ii) ∠QCP=150°

None

14.

In the adjoining figure, AB=AC=CD,∠ADC=35° Then (i) ∠ABC, (ii) ∠BEC are respectively:

Topic: Angles in an Isosceles Triangle and Circle/p>

70° and 70°.

80° and 60°.

10° and 50°.

70° and 40°.

None

15.

In the figure, two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If ∠APB = 70°, find ∠ACB .

Topic: Intersecting Circles and Angles

40°

30°

20°

50°

None

1 out of 15

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Class 9 Practice – Level 3 – Set 1 – Circles

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