20190305 F5 MC - photo.lkl.edu.hk

20190305 F.5 MC Practice (Geometry - Circles)

1

Level 1: single concept, simple calculation, easier than HKDSE types

Level 2: one or two concept, some calculations, similar to HKDSE easy types

Level 3: involving high level, logical and abstract thinking skills, or with

complicated calculations, similar to HKDSE difficult types

** Please answer any 30 questions **

Level 1

1.

In the figure, O is the centre. It is given that ∠BAC = 35°, find ∠BOC.

A. 35° B. 70° C. 80° D. 105°

2.

In the figure,⌢⌢

ACAB = and AB = 10 cm. Find the length of AC.

A. 10 cm B. 12 cm C. 14 cm D. 16 cm

3.

In the figure, O is the centre and AB // CD. Find ∠BAD.

A. 33.5° B. 39.5° C. 46.5° D. 57.5°

A

B

O

DC

E29°

84°

A

O

B C

35°°°°

A

B C


2

4.

In the figure, O is the centre of the semi-circle ACB. Find ∠ACB.

A. 50° B. 70° C. 80° D. 90°

5.

In the figure, O is the centre of the semi-circle ACB, if ∠ABC = 69° and

23=

⌢

AC , find⌢

CB .

A. 6 B. 7 C. 8 D. 9

6.

In the figure, O is the centre. If the sum of ∠ABC and ∠AOC is 258°, find x.

A. 16° B. 18° C. 20° D. 22°

7.

In the figure, ∠CAB = 36° and ∠ADB is two times of ∠CAB, find x.

A. 20° B. 24° C. 28° D. 36°

O A B

C

O

23

A B

C

69°


3

8.

In the figure, O is the centre. AOE is a straight line. Given that ∠AEC = 62° and

AC = CD, find ∠EAD.

A. 26° B. 28° C. 34° D. 36°

9.

In the figure, O is the centre. CEB is the diameter and AED is a straight line. Find

b.

A. 55° B. 58° C. 60° D. 62°

10.

In the figure, O is the centre and ∠CBD = 74°. Find ⌢⌢

BDCD : .

A. 36 : 47 B. 57 : 69 C. 69 : 48 D. 37 : 8

11.

In the figure, O is the centre of the semi-circle ADB, AB : DB = 5 : 3, find AB.

A. 4 cm B. 5 cm C. 6 cm D. 7 cm

B

C

D

E A O

62°

A

D C

B O

E b

74°

39°

D

A B O

4 cm

O

B

C

D

74°°°°


4

12.

In the figure, ABCD is a cyclic quadrilateral, x =

A. 24°. B. 28°. C. 48°. D. 56°.

13.

In the figure, a + b + c =

A. 180°. B. 360°. C. 540°. D. 720°.

14.

In the figure, z =

A. 30°. B. 65°. C. 90°. D. 95°.

15.

In the figure, a =

A. 40°. B. 50°. C. 65°. D. 85°.

B

AD

C

3y

2x

4y – 10°

x + 30°

A

B

C

D

E

F

ba

c

A

BC

E

Dz

30°

30° 95°

120°

80°°°° 15°°°°

65°°°° E

D

C

B

A


5

16.

In the figure, O is the centre, AB touches the circle at point A, x =

A. 30°. B. 45°. C. 60°. D. 75°.

17.

In the figure, TA is the tangent to the circle ABC. If ∠ACB = 28o and

∠ATB = 43o, find ∠ABC.

A. 54o B. 60o C. 65o D. 71o

18.

In the figure, O is the centre, the tangent ED to the circle meets the diameter

AOB produced at C. If ∠BCD = 24o, find ∠ADE.

A. 45o B. 48o C. 57o D. 66o

O

C

BA

x

A

C

T

B

43°°°° 28°°°°

C O B

A

E

D

24°°°°


6

19.

In the figure, PAB is a straight line and ST is the tangent to the circle at A. If

∠PAT = 38°, then ∠ACB =

A. 32°. B. 38°. C. 46°. D. 57°.

20.

In the figure, TP and TQ are tangents to the circle PQR at P and Q respectively.

If ∠RQP = 50° and ∠PTQ = 40°, then ∠RPQ =

A. 45°. B. 50°. C. 60°. D. 70°.

38°°°° P

T

A S

B

C

P

Q

R

T

40°°°° 50°°°°


7

Level 2

21.

In the figure, OE = OF = 5 cm and OC = 13 cm. Find the length of AB.

A. 12 cm B. 13 cm C. 24 cm D. 26 cm

23.

In the figure, OA // CB and ∠COA = 134°. Find ∠OAB.

A. 46° B. 67° C. 80° D. 113°

24.

In the figure, BD is a diameter of the circle. ∠ABD = 42° and ∠CBD = 38°. Find

∠DEC.

A. 76° B. 84° C. 86° D. 90°


8

25.

In the figure, O is the centre of the semi-circle ABCD. OB // DC and

∠AOE = 56°. Find ∠BAE.

A. 28° B. 34° C. 56° D. 62°

26.

In the figure, AD is a diameter of the circle. OC and BD intersect at P. AD

produced and BC produced meet at E. Find ∠OPB.

A. 50° B. 54° C. 67° D. 77°

27.

In the figure, AB = AC and ∠BAC = 22°. Find ∠ADC.

A. 79° B. 101° C. 102° D. 158°


9

28.

In the figure, AD // BC and ∠AEB = 60°. Find ∠ACB.

A. 30° B. 45° C. 60° D. 70°

29.

In the figure,

⌢⌢

ACAB = and ∠BOC = 130°. Find ∠OCA.

A. 32.5° B. 35° C. 65° D. 115°

30.

In the figure, AD is a diameter of the circle. AC cuts BD at E. AB = CD and

∠AEB = 64°. Find ∠EDA.

A. 26° B. 32° C. 52° D. 64°


10

31.

In the figure, DCQ is a straight line. ∠ODC = 70° and ∠BPC = 54°. Find

∠BCQ.

A. 54° B. 74° C. 106° D. 108°

32.

In the figure,

⌢⌢⌢⌢

DACDBCAB ::: = 6 : 4 : 3 : 5. Find ∠ABC.

A. 70° B. 80° C. 100° D. 120°

33.

In the figure, ABC and AEOD are straight lines. BA = BD and ∠BDC = 33°. Find

∠BAE.

A. 19° B. 20° C. 33° D. 57°


11

34.

In the figure, CT is the tangent to the circle at C. ABT is a straight line.

∠OAB = 20° and ∠CTB = 34°. Find ∠AOC.

A. 56° B. 112° C. 124° D. 144°

35.

In the figure, CT touches the circle at C. OC // AB and ∠OAB = 58°. Find ∠BCT.

A. 29° B. 32° C. 58° D. 61°

36.

In the figure, AT touches the circle at A. ∠BAT = 27°. If the circumference of the

circle is 40 cm, find the length of

⌢

AB .

A. 6 cm B. 7 cm C. 8 cm D. 9 cm


12

37.

In the figure, TA is the tangent to the circle at A. OT cuts the circle at B. OB = 20

and BT = 9. Find the length of TA.

A. 20 B. 21 C. 22 D. 23

38.

In the figure, AB, AC and PQ touch the circle at B, C and D respectively. PD = 7,

QD = 6 and AQ = 12. Find the length of AP.

A. 10 B. 11 C. 12 D. 13

39.

In the figure, a circle is inscribed in △ABC, where X, Y and Z are points of

contact. AB = 16 cm, AC = 34 cm and ∠ABC = 90°. Find the length of AZ.

A. 6 cm B. 10 cm C. 24 cm D. 30 cm


13

40.

In the figure, a circle is inscribed in △ABC, where X, Y and Z are points of

contact. AX = 14 cm, CZ = 15 cm and ∠ABC = 90°. Find the radius of the circle.

A. 6 cm B. 7 cm C. 8 cm D. 10 cm


14

Level 3

41.

In the figure, ABCD and AEO are straight lines. OC = 6 cm, BC = CD = 8 cm

and AE = 8.5 cm. Find the length of AB.

A. 8 cm B. 9 cm C. 9.5 cm D. 10 cm

42.

In the figure, AD = DB and CD ⊥ AB. AB = 32 cm and CD = 8 cm. Find the

radius of the circle.

A. 8 cm B. 12 cm C. 16 cm D. 20 cm

43.

In the figure, O is the centre of the semi-circle ABCDE. AC and BD intersect at

F.

⌢⌢⌢

CDBCAB == and ∠AOD = 120°. Find ∠AFD.

A. 100° B. 120° C. 140° D. 150°


15

44.

In the figure, O is the centre. OC and AB intersect at a point D and AD = BD.

Which of the following must be true?

I. DC ⊥ AB II. AC = BC III. OD = DC

A. I only B. II only C. I and II only D. I, II and III

45.

In the figure, O is the centre, if AB = AC = 4 and BC = 1, which of the following

is/are incorrect?

I. 2∠BOC = ∠AOC II. ⌢⌢

ABAC =

III. △AOB ∼ △AOC

A. I only B. I and III only

C. II and III only D. I, II and III

O

A

B C

4

1

4


16

46.

In the figure, CD is a diameter of the circle. ∠BAC = 48°, ∠ABD = 158° and

∠BDC = 68°. Which of the following is/are true?

I. AB is the tangent to the circle at B.

II. AC is the tangent to the circle at C.

III. AB = AC

A. I only B. II only C. I and III only D. I, II and III

47.

In the figure, PQ and QR are the tangents to the circle at two points A and B

respectively. If BC = CD, ∠BAD = 76° and ∠ADC = 106°, find ∠AQB.

A. 30° B. 40° C. 44° D. 53°


17

48.

In the figure, O is the centre of the circle. ADO is a straight line. AC is the

tangent to the circle at point C. B is a point lying on AC such that AB = BC.

⌢

CED = 5⌢

DC . Which of the following must be true?

I. △OCD is an equilateral triangle.

II. AD = OD

III. AD = 2DB

A. II only B. I and III only

C. II and III only D. I, II and III

49.

In the figure, O is the centre of the circle. AOCD, BFC and OFE are straight

lines. ED is the tangent to the circle at point E and ED // BC. If OA = 30 and

AB = 36, then ED =

A. 36. B. 40. C. 48. D. 50.


18

50.

In the figure, AEC and BED are straight lines. AB // DC and DE = CE. Which of

the following must be true?

I. A, B, C and D are concyclic.

II. AE = DE

III. ∠ADC = ∠BCD

A. I only B. III only C. I and III only D. II and III only

Full Solution:

20190305 F5 MC - photo.lkl.edu.hk

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