Quiz about Right Triangles Tangents and Circles

Question 1

Find x

Accepted Answer

10

Answer

5

Answer

18

Answer

9

Question 2

Use chords to solve for x

Accepted Answer

x = 6 cm

Answer

x = 3 cm

Answer

x = 4 cm

Answer

x = 6 in

Question 3

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?"

Accepted Answer

15

Answer

-15

Answer

6

Answer

14

Question 4

In the diagram, the straight lines AB and CD are parallel.

Find the value of x.

Accepted Answer

p

Answer

r

Answer

s

Answer

q

Question 5

The diagram shows a circle with centre O.

Among the angles p, q, r and s, which of the following does not have the same size in angle?

Accepted Answer

q

Answer

r

Answer

s

Answer

p

Question 6

The diagram shows a circle with centre, O.

KML and MON are straight lines.

Find the length of the line MON.

Accepted Answer

18

Answer

12

Answer

22

Answer

24

Question 7

In the diagram, P and R are the centres of the circles. $$\Delta QST$$ is an equilateral triangle.
Find the length of PQR.

Accepted Answer

Answer

Answer

Answer

Question 8

In the diagram, O is the centre of the circle QPRLS. The radius OL bisects the chords PQ and RS respectively at T and K.

Given that PQ = 30 cm, find the length of KT.

Accepted Answer

7

Answer

4

Answer

5

Answer

6

Question 9

In the diagram, T and R are the cetres of two circles of equal size which touch at point Q.

Find the length of the line PTQRS.

Accepted Answer

36

Answer

18

Answer

24

Answer

30

Question 10

In the diagram, O is the centre of the circle.

What is the value of x?

Accepted Answer

$$240\degree$$

Answer

$$60\degree$$

Answer

$$120\degree$$

Answer

$$300\degree$$

Question 11

In the diagram, O is the centre of the circle and POQ is a straight line.

Find the value of y.

Accepted Answer

$$85\degree$$

Answer

$$60\degree$$

Answer

$$90\degree$$

Answer

$$100\degree$$

Question 12

In the diagram, O and V are the centres of two circles that touch each other.

Find the value of a+b.

Accepted Answer

160

Answer

120

Answer

100

Answer

90

Question 13

In the diagram, PQTS and MTN are straight lines.

Find the value of y.

Accepted Answer

$$14\degree$$

Answer

$$10\degree$$

Answer

$$20\degree$$

Answer

$$70\degree$$

Question 14

In the diagram, PYORQ is the diameter of a circle with the centre O. XRT and XYZ are the chords of the circle. Find the value of y.

Accepted Answer

$$50\degree$$

Answer

$$30\degree$$

Answer

$$40\degree$$

Answer

$$45\degree$$

Question 15

In the diagram, O is the centre of the circle. ORQ and PRS are straight lines.

Find the value of a+b.

Accepted Answer

80

Answer

60

Answer

70

Answer

100

Question 16

In the diagram, ABCD is the diameter of the circle.

What is the value of y?

Accepted Answer

$$35\degree$$

Answer

$$20\degree$$

Answer

$$25\degree$$

Answer

$$30\degree$$

Question 17

In the diagram, PQRS and TQV are straight lines.

Find the value of y.

Accepted Answer

40

Answer

70

Answer

60

Answer

20

Question 18

In the diagram, PQRS is a cyclic quadrilateral and TSQU is a straight line. Find the value of x.

Accepted Answer

$$120\degree$$

Answer

$$70\degree$$

Answer

$$170\degree$$

Answer

$$240\degree$$

Question 19

In the diagram, PQ is a diameter and PQRS is a cyclic quadrilateral.
Find the value of $$k+y$$ .

Accepted Answer

$$150\degree$$

Answer

$$60\degree$$

Answer

$$120\degree$$

Answer

$$270\degree$$

Question 20

In the diagram, PQRS is a cyclic quadrilateral and RST is a straight line.
Find the value of $$p+q$$

Accepted Answer

$$36\degree$$

Answer

$$60\degree$$

Answer

$$120\degree$$

Answer

$$220\degree$$

Question 21

In the diagram, QT is a tangent to the circle, at T, with centre O.

Find the value of x.

Accepted Answer

40

Answer

25

Answer

30

Answer

50

Question 22

In the diagram, PT and QT are tangents to the circle with centre O.

Which of the following statements is false?

Accepted Answer

$$x+y=360\degree$$

Answer

Answer

$$\angle PTO=\angle QTO$$

Answer

$$\Delta POT$$ and $$\Delta QOT$$ are congruent

Question 23

In the diagram, PQR is a tangent to the circle with centre O and SOR is a straight line.

Find the value of x.

Accepted Answer

18

Answer

20

Answer

30

Answer

45

Question 24

In the diagram, RS is a tangent to the circle with centre O and PQR is a straight line.

Find the value of x.

Accepted Answer

40

Answer

30

Answer

50

Answer

80

Question 25

In the diagram, PT and QT are tangents to the circle with centre O.

Find the perimeter of OPTQ.

Accepted Answer

46

Answer

38

Answer

40

Answer

48

Question 26

In the diagram, QRT is a tangent to the circle with centre O, at R. RUS and OUPT are straight lines.

Find the value of x.

Accepted Answer

25

Answer

35

Answer

45

Answer

30

Question 27

In the diagram, JKL is a tangent to the circle.
Given that KN is a diameter and $$\angle KNM=55\degree$$ , find the value of $$\angle JKM$$ .

Accepted Answer

$$125\degree$$

Answer

$$120\degree$$

Answer

$$135\degree$$

Answer

$$145\degree$$

Question 28

In the diagram, RST is a tangent to the circle with centre O.

Find the value of y.

Accepted Answer

55

Answer

50

Answer

60

Answer

65

Question 29

In the diagram, PT is a tangent to the circle at T and O is the centre.
Find the value of $$x+y$$ .

Accepted Answer

Answer

Answer

Answer

Question 30

In the diagram, PQ is a tangent to the circle QRST.

Find the value of z.

Accepted Answer

80

Answer

65

Answer

55

Answer

50

Question 31

In the diagram, RST is a tangent to the circle at S and QPT is a straight line.

Find the value of k.

Accepted Answer

27

Answer

37

Answer

42

Answer

69

Question 32

In the diagram, PQ is the common tangent to the two circles with centres O and V respectively.

Given that OP = 10 cm, PQ = 24 cm and the distance between the two centres is 25 cm. Find the length of QV.

Accepted Answer

17

Answer

13

Answer

15

Answer

20

Question 33

In the diagram, PQR is a tangent to the circle QSV at point Q. QVU is a straight line.

Find the value of y.

Accepted Answer

100

Answer

80

Answer

90

Answer

110

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