Topics
28. Circle Geometry
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iGCSE (2021 Edition)

28.01 Chords and arcs

Lesson
Worksheet
Practice
Worksheet
Missing angles
1

In the given diagram, AC is a straight line passing through centre O:

Solve for x.

2

Consider the circle with centre O shown:

Solve for x.

Missing angles (Extended)
3

For each of the following circles with centre O, solve for x:

a
b
c
4

For each of the following circles, solve for x :

a
b
c
5

For each of the following circles with centre O, solve for x:

a
b
c
Missing lengths
6

Consider the following circle where O is the centre:

Find the length AB.

7

For each of the following circles with centre O, solve for x:

a
b
c
8

The given circle has TR = 12\text{ cm}, the radius is 13\text{ cm}, and OR has length h\text{ cm}.

Find the area of \triangle TOV.

9

The diagram shows AC as the arc of a circle with O as its centre, OB = 9, and AB = 7:

a

Find the exact length of OA.

b

Hence, find the exact length of BC.

Missing lengths (Extended)
10

For each of the following circles with centre O, solve for x:

a
b
c
11

Consider the following circle where O is the centre:

a

Solve for t.

b

Solve for u.

Proofs
12

Let O be the centre of the given circle with AB = CD.

a

Prove that \triangle ABO and \triangle CDO are congruent.

b

Hence, prove that \triangle BEO and \triangle DFO are congruent.

13

(Extended)

Let O be the centre of the given circle:

Prove that x and y are complementary angles.

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Outcomes

0580C4.7E

Calculate unknown angles using the property of an angle in a semicircle.

0580E4.6

Recognise rotational and line symmetry (including order of rotational symmetry) in two dimensions. Recognise symmetry properties of the prism (including cylinder) and the pyramid (including cone). Use the following symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the centre • tangents from an external point are equal in length.

0580E4.7E

Calculate unknown angles using the property of an angle in a semicircle.

0580E4.7H

Calculate unknown angles using the following geometrical properties: • angle at the centre of a circle is twice the angle at the circumference. • angles in the same segment are equal.

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