1. Chapter 5 Properties of Circles

2. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Terminology about Circle Centre Circumference Chord Radius Diameter

3. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Terminology about Circle Minor arcMajor arc

4. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Terminology about Circle Minor segment Major segment

5. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Terminology about Circle Sector Semi-circle

6. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Properties of Chords (I) What is the relation between AM and BM when OM  AB?

7. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Properties of Chords (I) AM  BM

8. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Properties of Chords (II) What is the relation between ON and OM when AB  CD?

9. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Properties of Chords (II) ON  OM

10. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Arcs and Angles at the Centre

11. 2004 Chung Tai Educational Press © Chapter Examples Quit 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?

12. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles 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?

13. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Angles in a Circle  AOB  2  ACB If AOB is a diameter, then  ACB  90 .

14. 2004 Chung Tai Educational Press © Chapter Examples Quit 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

15. 2004 Chung Tai Educational Press © Chapter Examples Quit 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

16. 2004 Chung Tai Educational Press © Chapter Examples Quit 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

17. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Arcs and Angles at the Circumference

18. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles Cyclic Quadrilaterals What are the relations among the interior angles of a cyclic quadrilateral? Which angle equals  BCE?

19. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles  BAD   BCD  180   ADC   ABC  180   BCE   BAD Cyclic Quadrilaterals

20. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles What is the relation between tangent PQ and radius OT? Point of contact Tangents to a Circle

21. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles OT  PQ Tangents to a Circle

22. 2004 Chung Tai Educational Press © Chapter Examples Quit 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

23. 2004 Chung Tai Educational Press © Chapter Examples Quit 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?

24. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 5 Properties of Circles  BAC   BCD Angles in the Alternate Segment

25. End