PowerPoint Chapter 5
Terminology about Circle
Terminology about Circle
Terminology about Circle
Terminology about Circle
Arcs and Angles at the Centre
What is the relation between arcs and angles at the centre subtended by the arcs in a circle?
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Arcs and Angles at the Centre
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Angles in a Circle
What is the relation between the angle at the centre (AOB) and the angle at the circumference (ACB) subtended by the same arc?
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Angles in a Circle
AOB = 2ACB
Angles in a Circle
Assume AB is fixed. When point C moves along the circumference of a segment, does ACB change?
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Angles in a Circle
ACB does not change.
i.e. angles in the same segment of a circle are equal.
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Arcs and Angles at the Circumference
What is the relation between arcs and angles at the circumference subtended by the arcs in a circle?
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Arcs and Angles at the Circumference
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Cyclic Quadrilaterals
What are the relations among the interior angles of a cyclic quadrilateral? Which angle equals BCE?
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Cyclic Quadrilaterals
Properties of Chords (I)
What is the relation between AM and BM when OM AB?
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Properties of Chords (I)
Properties of Chords (II)
What is the relation between ON and OM when AB = CD?
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Properties of Chords (II)
Tangents to a Circle
What is the relation between tangent PQ and radius OT?
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Tangents to a Circle
Tangents to a Circle
TP and TQ are the tangents to the circle at P and Q respectively.
TP = TQ
TOP = TOQ
PTO = QTO
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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?
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BAC = BCD
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