Free Printable Form 3 Chapter 6 Angles and Tangents of circles

1.

Calculate the value of x

(a)

2.

Determine the value of y

(a)

3.

Determine the value of x

(a)

4.

Calculate the value of x

(a)

5.

Calculate the value of x

(a)

6.

Calculate the value of x

(a)

7.

Calculate the value of x

(a)

8.

Find the value of y

(a)

9.

Calculate the radius of the circle correct to 2 dp

(a)

10.

The diagram shows a circle with centre O. Find the value of x.

a)

$80\degree$

b)

$100\degree$

c)

$140\degree$

d)

$280\degree$

11.

The diagram shows a circle. The arcs of BC and DE are of equal length. Find the value of x.

a)

$90\degree$

b)

$100\degree$

c)

$120\degree$

d)

$130\degree$

12.

In the diagram, PQ and RST are two parallel straight lines. Find the value of x.

a)

$100\degree$

b)

$110\degree$

c)

$120\degree$

d)

$130\degree$

13.

The diagram shows a circle with centre O. SQT is a tangent to the circle at point Q. Find the value of x.

a)

$40\degree$

b)

$50\degree$

c)

$55\degree$

d)

$60\degree$

14.

In the diagram, ORQ is a straight line and PQ is a tangent to the circle with centre O at point P. Find

\angle PQO

a)

$28\degree$

b)

$32\degree$

c)

$34\degree$

d)

$46\degree$

15.

In the diagram, PQR and PST are tangents to the circle with centre O at Q and S respectively. Find the value of x.

a)

$66\degree$

b)

$68\degree$

c)

$72\degree$

d)

$76\degree$

16.

In the diagram, PQR is a tangent to the circle with centre O, at Q and

$\angle SQR\ =\ 68\degree.\ Find\ the\ value\ of\ y.$

a)

$20\degree$

b)

$22\degree$

c)

$24\degree$

d)

$25\degree$

17.

The diagram shows a circle with centre O. Determine the value of angles of q.

(only write number)

(a)

18.

In the diagram, ABCD is a cyclic quadrilateral. BOD is a diameter of circle with centre O and CDE is a straight line. Choose the correct relation based on the diagram given.

a)

$\angle ADE\ =\ \angle ABD$

b)

$\angle ABD\ +\angle BDA\ =\ 90\degree$

19.

In the diagram, PTR and QTS are straight lines. Find the value of x.

a)

28

b)

32

c)

36

d)

48

20.

Choose the correct cyclic quadrilateral for JKLM. You can choose more than one answer.

a)

b)

c)

d)

21.

Identify the straight lines that are tangents to the circle in the diagram. You can choose more than one answer.

a)

AB

b)

RS

c)

KJ

d)

LM

e)

TU

22.

State the angles of equal size in the diagram. You can choose more than one answer.

a)

$w=y$

b)

$w=x$

c)

$x=y$

23.

Determine the value of x in the diagram.

*eg: 70

(a)

24.

In the diagram, ABC is a straight line. Choose the correct statement below. You can choose more than one answer.

a)

$t\degree+r\degree=180\degree$

b)

$q\degree+r\degree+s\degree+t\degree=360\degree$

25.

In the diagram, PQ and QR are tangents to a circle at P and R respectively. Which of the following statements is correct?

a)

$PQ\ne RQ$

b)

$OQ=\sqrt{RO+QR}$

c)

$\angle PQO=\angle ROQ$

d)

$\angle POQ=\angle QOR$

26.

Find the value of z

(a)

27.

Determine the value of x

(a)

28.

Find the value of y

(a)

29.

Name the properties of a circle.

W = _____________ and X = _______________

a)

W = Minor arc and X = Major arc

b)

W = Major arc and X = Minor arc

c)

W = Major sector and X = Minor sector

d)

W = Minor sector and X = Major sector

30.

RS is a common tangents to the two circle with centres P and Q respectively.Find the value of x.

RS ialah tangen sepunya bagi dua buah bulatan masing-masing dengan pusat P dan Q.Cari nilai x.

(a)

31.

How many common tangents?

a)

0

b)

1

c)

2

d)

3

e)

4

32.

How many common tangents?

a)

0

b)

1

c)

2

d)

3

e)

4

33.

How many common tangents?

a)

0

b)

1

c)

2

d)

3

e)

4

34.

Diagram shows a tangent to a circle.

a)

True

b)

False

35.

A tangent line intersects the circle ...

a)

in exactly two points

b)

in exactly one point

c)

through the center

d)

with the diameter

36.

Which shows a tangent line?

a)

b)

c)

d)

37.

If a line is tangent to a circle, then it is ________ to the radius drawn to the point of tangency.

a)

parallel

b)

adjacent

c)

supplementary

d)

perpendicular

38.

Using the tangent lines, find the value of x.

a)

60

b)

120

c)

30

d)

300

39.

Using lines tangent to the circle, find the value of x.

a)

57

b)

137

c)

47

d)

257

40.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

c)

Not sure

41.

Determine if a tangent line is shown in the picture.

a)

Yes

b)

No

c)

Not Sture

42.

Assume that the lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x to the nearest tenth.

a)

11.7

b)

10.8

c)

13.0

d)

14.2

43.

Assume that the lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x to the nearest tenth.

a)

4.1

b)

5.8

c)

4.7

d)

3.6

44.

Angles at the circumference subtended by arcs of the same length are ..........

a)

equal

b)

not equal

45.

The size of an angle at the circumference subtended by an arc is ............ to the arc length

a)

equal

b)

not equal

c)

proportional

d)

not proportional

46.

State the value of x

(a)

47.

The size of the angle at the centre of a circle subtended by the same arc is twice the size of angle at the circumference.

Which diagram represents the statement given?
(You can choose more than 1 answer)

a)

b)

c)

d)

48.

Determine the value of x and y.

a)

$x\ =\ 80\degree,\ y\ =\ 80\degree$

b)

$x\ =\ 80\degree,\ y\ =\ 40\degree$

c)

$x\ =\ 40\degree,\ y\ =\ 80\degree$

d)

$x\ =\ 40\degree,\ y\ =\ 40\degree$

49.

Calculate the value of y.

a)

$55\degree$

b)

$110\degree$

50.

The angle at the circumference of circle subtended by the diameter is (a) $\degree$

51.

Are the size of angle x, y and z the same?

a)

No, because the angles are not at the circumference of the circle

b)

Yes, because the arc length is the same

c)

Yes, because the height angles x,y and z is the same

d)

No, because the arc length is proportional

52.

If AB = 3FE , determine the value of x

a)

$30\degree$

b)

$20\degree$

c)

$25\degree$

d)

$35\degree$

53.

Find the value of x

a)

$100\degree$

b)

$94\degree$

c)

$104\degree$

d)

$110\degree$

54.

Find the value of x

a)

$115\degree$

b)

$120\degree$

c)

$100\degree$

d)

$105\degree$

55.

Given that $\angle\ SQR\ =\ 55\degree$ and length of OQ = 7 cm. Find $\angle\ SOQ$

a)

$110\degree$

b)

$120\degree$

c)

$100\degree$

d)

$115\degree$

56.

Calculate the value of x+y

a)

$90\degree$

b)

$122\degree$

c)

$110\degree$

d)

$132\degree$

57.

Calculate y - x

a)

$20\degree$

b)

$22\degree$

c)

$12\degree$

d)

$8\degree$

58.

Which of the following has three common tangents

a)

b)

c)

d)

59.

Calculate $\angle\ OQR$

a)

$30\degree$

b)

$40\degree$

c)

$24\degree$

d)

$20\degree$

60.

The diagram shows two wheels of the same size which are connected by a belt drive. Given the length of PQ is 40cm and the diameter of each wheel is 23cm. Calculate the length in cm of the belt drive.

( use $\pi\ =\ 3.142\$ )

a)

145.34

b)

155.24

c)

140.25

d)

152.26

Form 3 Chapter 6 Angles and Tangents of circles

Total questions: 60

Worksheet time: 3hrs 24mins

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