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iGCSE (2021 Edition)

23.01 Chords and arcs

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

0607C5.6B

Pythagoras’ Theorem in two dimensions Including chord length and distance of a chord from the centre of a circle.

0607C5.7B

Use and interpret vocabulary of circles. Angle in a semicircle property.

0607E5.6B

Pythagoras’ Theorem and its converse in two dimensions including chord length and distance of a chord from the centre of a circle.

0607E5.7B

Use and interpret vocabulary of circles. Angle in a semicircle property.

0607E5.7C

Properties of circles: angles at the centre and at the circumference on the same arc.

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