#### Geometry Model Question Paper

9th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
5 x 1 = 5
1. PQ and RS are two equal chords of a circle with centre O such that ㄥPOQ=70°, then ㄥOR

(a)

60°

(b)

70°

(c)

55°

(d)

80°

2. In a cyclic quadrilaterals ABCD, ㄥA=4x,ㄥC=2x the value of x is

(a)

30°

(b)

20°

(c)

15°

(d)

25°

3. In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ㄥQR = 80°, then ㄥTVS=

(a)

80°

(b)

100°

(c)

70°

(d)

90°

4. If one angle of a cyclic quadrilateral is 75° , then the opposite angle is

(a)

100°

(b)

105°

(c)

85°

(d)

90°

5. AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24cm then the distance of AB from the centre of the circle is

(a)

10cm

(b)

9cm

(c)

8cm

(d)

6cm

6. 5 x 1 = 5
7. Twice of the radius is called _______ of the circle

()

diameter

8. Longest chord passes through the _______ of the circle.

()

centre

9. Distance from the centre to any point on the circumference of the circle is called ____

()

10. A part of a circle between any two points is called a/an ________ of the circle

()

arc

11. A circle divides the plane into ________ parts.

()

three

12. 5 x 1 = 5
13. Line segment joining any two points on the circle is called radius of the circle.

(a) True
(b) False
14. Point of concurrency of the diameter is the centre of the circle

(a) True
(b) False
15. The boundary of the circle is called its circumference

(a) True
(b) False
16. A circle has infinite number of equal chords

(a) True
(b) False
17. Sector is the region between the chord and its corresponding arc

(a) True
(b) False
18. 8 x 2 = 16
19. The radius of the circle is 25cm and the length of one of its chord is 40cm. Find the distance of the chord from the centre

20. The chord of length 30 cm is drawn at the distance of 8cm from the centre of the circle. Find the radius of the circle

21. A chord is 12cm away from the centre of the circle of radius 15cm. Find the length of the chor

22. 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

23. In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ㄥDBC=40° and ㄥBAC=60°

24. The arch of a bridge has dimensions as shown, where the arch measure 2m at its highest point and its width is 6m. What is the radius of the circle that contains the arch?

25. In the given figure, ㄥPOQ=1000 and ㄥPQR=300, then find ㄥRPO

26. Draw a right triangle whose hypotenuse is 10 cm and one of the legs is 8 cm. Locate its incentre and also draw the incircle

27. 3 x 3 = 9
28. If O is the centre of the circle and ㄥABC=30° then find ㄥAOC.

29. Construct the ΔLMN such that LM=7.5cm, MN=5cm and LN=8cm. Locate its centroid.

30. Construct the ΔPQR such that PQ = 5cm, PR= 6cm and ㄥQP = ° R 60 and locate its centroid

31. 2 x 5 = 10
32. Find the length of a chord which is at a distance of 2 $\sqrt{11}$ confrom the centre of a circle of radius 12cm

33. Construct the incentre of ΔABC with AB = 6 cm, ㄥB=65° and AC = 7 cm Also draw the incircle and measure its radius.