REVISION WORKSHEET 1

CHAPTER- 10 CIRCLES
SUBJECT: MATHEMATICS MAX. MARKS : 40
CLASS : IX DURATION : 1½ hrs (a) 22° (b) 33° (c) 44° (d) 68°
General Instructions:
(i). All questions are compulsory. 6. In figure, ∠AOB = 90° and ∠ABC = 30°, then ∠CAO is equal to
(ii). This question paper contains 20 questions divided into five Sections A, B, C, D and E.
(iii). Section A comprises of 10 MCQs of 1 mark each. Section B comprises of 4 questions of 2 marks
each. Section C comprises of 3 questions of 3 marks each. Section D comprises of 1 question of 5
marks each and Section E comprises of 2 Case Study Based Questions of 4 marks each.
(iv). There is no overall choice.
(v). Use of Calculators is not permitted

SECTION – A (a) 30° (b) 45° (c) 90° (d) 60°

Questions 1 to 10 carry 1 mark each.
7. In the given figure, ∠DBC = 55°, ∠BAC = 45° then ∠BCD is
1. In figure, if ∠ABC = 20°, then ∠AOC is equal to:

(a) 45° (b) 55° (c) 100° (d) 80°

8. In the given figure, O is the centre of the circle, ∠CBE = 25° and ∠DEA = 60°. The measure
(a) 20° (b) 40° (c) 60° (d) 10° of ∠ADB is

2. In the given figure, value of x is

(a) 90° (b) 85° (c) 95° (d) 120°

(a) 140° (b) 70° (c) 110° (d) 280° In the following questions 9 and 10, a statement of assertion (A) is followed by a statement of
Reason (R). Choose the correct answer out of the following choices.
3. In the given figure, O is the centre of the circle. The value of x is (a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

9. Assertion (A): In the given figure, ∠ABC = 70° and ∠ACB = 30°. Then, ∠BDC = 80°.
(a) 140° (b) 70° (c) 290° (d) 210°

4. Given a circle of radius 5 cm and centre O. OM is drawn perpendicular to the chord XY. If OM = 3
cm, then length of chord XY is
(a) 4 cm (b) 6 cm (c) 8 cm (d) 10 cm

5. In the given figure, O is centre of the circle, ∠BAO = 68°, AC is diameter of the circle, then measure
of ∠BCO is Reason (R): Angles in the same segment of a circle are equal.

10. Assertion (A): If O is the centre of the circle as shown in figure, then CBD = 55°.

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 16. In the given figure, O is the centre of the circle with radius 5 cm. OP AB, OQ CD, AB || CD, AB
= 6 cm and CD = 8 cm. Determine PQ.

Reason (R): Exterior angle of cyclic quadrilateral is equal to interior opposite angle

SECTION – B 17. In the given figure, O is the centre of the circle and AOB = 110°, find the value of x, y and z.
Questions 11 to 14 carry 2 marks each.
11. In the given figure, ABCE is a cyclic quadrilateral and O is the centre of circle. If AEC = 110°,
then find (a) ABC (b) ADC

SECTION – D
Questions 18 carry 5 marks.
18. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point
12. In the given figure, ADC = 130° and chord BC = chord BE. Find CBE. on the remaining part of the circle.
OR

In a circle of radius 18 cm, AB and AC are two chords such that AB = AC = 12 cm. Find the length
of chord BC.

SECTION – E (Case Study Based Questions)

Questions 19 to 20 carry 4 marks each.
19. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m
13. In the given figure, ΔABC is equilateral. Find BDC and BEC. drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. The distance
between Reshma and Salma and between Salma and Mandip is 6m each. In the given below figure
Reshma’s position is denoted by R, Salma’s position is denoted by S and Mandip’s position is
denoted by M.

14. If two chords of a circle are equally inclined to the diameter passing through their point of
intersection, prove that the chords are equal.

SECTION – C
Questions 15 to 17 carry 3 marks each.
15. In the given figure, AB is diameter of the circle with centre O and CD || AB. If DAB = 25°, then
find the measure of CAD.

(i) Find the area of triangle ORS. [2]

(ii) What is the distance between Reshma and Mandip? [2]
OR

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 (ii) If BC is a diameter of a circle of centre O and OD is perpendicular to the chord AB of a circle,
show that CA = 2OD. [2]

20. Aditya seen one circular park in which two triangular ponds are there whose common vertex is the
centre of the park. After coming back to home, he tried to draw the circular park on the paper. He
draws a circle of radius 10 cm with the help of a compass and scale. He also draws two chords, AB
and CD in such a way that the perpendicular distance from the center to AB and CD are 6 cm and 8
cm respectively. Now, he has some doubts that are given below.

(i) Show that the perpendicular drawn from the Centre of a circle to a chord bisects the chord using
any one triangle. (2)
(ii) What is the length of CD? (2)
OR
(ii) What is the length of AB? (2)

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