chapter 5 properties of circles. 2004 chung tai educational press © chapter examples quit chapter 5...
TRANSCRIPT
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
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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
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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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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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BAD BCD 180ADC ABC 180
BCE BAD
Cyclic Quadrilaterals
2004 Chung Tai Educational Press©
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What is the relation between tangent PQ and radius OT?
Point of contact
Tangents to a Circle
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OT PQ
Tangents to a Circle
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TP and TQ are the tangents to the circle at P and Q respectively.
TP TQ
TOP TOQ
PTO QTO
Tangents to a Circle
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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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BAC BCD
Angles in the Alternate Segment
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