chapter 5 properties of circles. 2004 chung tai educational press © chapter examples quit chapter 5...
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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©
Chapter Examples
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Chapter 5 Properties of Circles
Terminology about Circle
Minor arc Major arc
2004 Chung Tai Educational Press©
Chapter Examples
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Chapter 5 Properties of Circles
Terminology about Circle
Minor segment
Major segment
2004 Chung Tai Educational Press©
Chapter Examples
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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©
Chapter Examples
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Chapter 5 Properties of Circles
Properties of Chords (I)
AM BM
2004 Chung Tai Educational Press©
Chapter Examples
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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©
Chapter Examples
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Chapter 5 Properties of Circles
Properties of Chords (II)
ON OM
2004 Chung Tai Educational Press©
Chapter Examples
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Chapter 5 Properties of Circles
BOCAOCCBCA ::
Arcs and Angles at the Centre
2004 Chung Tai Educational Press©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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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©
Chapter Examples
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Chapter 5 Properties of Circles
BAC BCD
Angles in the Alternate Segment
EndEnd
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