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Chapter 5Chapter 5

Properties of CirclesProperties of Circles

2004 Chung Tai Educational Press©

Chapter Examples

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Chapter 5 Properties of Circles

Terminology about Circle

Centre

Circumference

Chord

Radius

Diameter

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Terminology about Circle

Minor arc Major arc

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Terminology about Circle

Minor segment

Major segment

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Terminology about Circle

Sector

Semi-circle

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Properties of Chords (I)

What is the relation between AM and BM when OM AB?

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Properties of Chords (I)

AM BM

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Properties of Chords (II)

What is the relation between ON and OM when AB CD?

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Properties of Chords (II)

ON OM

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

BOCAOCCBCA ::

Arcs and Angles at the Centre

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Arcs and Angles at the Centre

What is the relation between arcs and angles at the centre subtended by the arcs in a circle?

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Angles in a CircleWhat is the relation between the angle at the centre (AOB) and the angle at the circumference (ACB) subtended by the same arc?

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Angles in a Circle

AOB 2ACB

If AOB is a diameter, then ACB 90.

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Assume AB is fixed. When point C moves along the circumference of a segment, does ACB change?

Angles in a Circle

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

ACB does not change.

i.e. angles in the same segment of a circle are equal.

Angles in a Circle

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

What is the relation between arcs and angles at the circumference subtended by the arcs in a circle?

Arcs and Angles at the Circumference

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Arcs and Angles at the Circumference

BDCADBCBBA ::

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Cyclic Quadrilaterals

What are the relations among the interior angles of a cyclic quadrilateral? Which angle equals BCE?

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

BAD BCD 180ADC ABC 180

BCE BAD

Cyclic Quadrilaterals

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

What is the relation between tangent PQ and radius OT?

Point of contact

Tangents to a Circle

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

OT PQ

Tangents to a Circle

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

TP and TQ are the tangents to the circle at P and Q respectively.

TP TQ

TOP TOQ

PTO QTO

Tangents to a Circle

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

Angles in the Alternate Segment

If CD is the tangent to the circle at C, what is the relation between BAC and BCD?

2004 Chung Tai Educational Press©

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Chapter 5 Properties of Circles

BAC BCD

Angles in the Alternate Segment

EndEnd

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