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Stage 5.1-3

5.05 Cyclic quadrilaterals

Worksheet
Cyclic quadrilaterals
1

Consider the diagram where ABCD is inscribed inside a circle.

a

State the sum of any two opposite angles in the quadrilateral ABCD.

b

Can a parallelogram without right angles be inscribed inside a circle?

2

State whether the following are cyclic quadrilaterals:

a
b
c
d
e
f
3

Find m in the given diagram:

4

Consider the given diagram:

a

Find x.

b

Find y.

5

The quadrilateral ABCD has vertices that lie on a circle:

Suppose that the diagonals AC and BD pass through the center of the circle, determine whether the following statements are true or false:

a

ABCD must be a square, but might not be a parallelogram.

b

ABCD must be a parallelogram, but might not be a trapezium.

c

ABCD must be a parallelogram, but might not be a rectangle.

d

ABCD must be a rectangle, but might not be a square.

6

Consider the given diagram.

Show all working and reasoning to determine the value of y.

7

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

Show all working and reasoning and find the size of angles:

a

p

b

q

c

r

8

In the given diagram, O is the centre of the circle. Find the size of angles x and y.

Show all working and reasoning.

9

In the figure below, the two circles intersect at points B and E.

If \angle BCD = 104\degree, find \angle BAF. Show all working and reasoning.

10

In the given diagram, the angles \angle PSA and \angle AQR are congruent angles and the variable y represents the reflex angle at the centre point A:

Find the size of angle x.

Show all working and reasoning.

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Outcomes

MA5.3-17MG

applies deductive reasoning to prove circle theorems and to solve related problems

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