The Chinese University of Hong Kong EDD 5161

The Chinese University of Hong Kong EDD 5161 F Educational Communications and Technology Group 14

Mathematics Target Audience: F. 4 Science Students Duration: 2 lessons Topic: Basic Properties of Circles

Basic Properties of Circles n Basic terms of a circle n. Angles at centre and circumference n Angles in the semi-circle n Angles in the same segment

I. Basic Terms of a Circle B Segment A C Chord O D Diameter Arc E Radius

II. Angles at centre and circumference x y y = 2 x Reference: at centre = 2 at circumference

Proof: x = 2 m m n x y = 2 n y x + y = 2 (m+n) at centre = 2 ( at circumference)

Illustrative example: Find x and y x O y at centre twice at circumference

Quiz: Q. 1 y A. O B. C. D. E.

Q. 2 A. O B. x C. D. E.

III. Angle in the semi-circle B A O Reference: in the semi-circle C

Proof: C A O B at centre twice at circumference

Illustrative example: x z in the semi-circle O ( base s, isos )

IV. Angle in the segment x y x=y Reference: in the same segment

Proof: z = 2 x x y O z at centre twice at circumference z = 2 y at centre twice at circumference x=y

Illustrative example: A D in the same segment O y C in the semi-circle B sum of

Quiz: Find x and y Q. 1 y in the same segment x in the same segment

Q. 2 A. x B. C. D. E.

Revision on the properties of circles x in the same segment y B A C O x y in the semi-circle at centre = 2 at circumference

T H E E ND

Prepared by Name Chan Chi Man Benjamin Wong Kwong Leung Chan Mei Ling Student No. 98040300 98118940 97043700