Everything Maths Grade 12

CHAPTER 9. GEOMETRY 9.2

1. 2.

3. 4.

�

�

R

Q

S

3 cm

�

�

A

B

C

D

E

F

G

H

I

J

K

L

M N

O

P

AE = 5 cm

AC = 8 cm

a CE = 9 cm

b

c

�

�

�

d

(^5) cm
8 cm
(^2) cm
6 cm
e
f
LN = 7. 5 cm
More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 0226 (2.) 0227 (3.) 0228 (4.) 0229

Theorem 10. The angle between a tangent and a chord, drawn at the point of contactof the chord, is
equal to the angle which the chord subtends inthe alternate segment.

Proof:

O�

A

B

P

Q

T

S R

Consider a circle, with centre O. Draw a chord AB and a tangent SR to the circle at point B. Chord
AB subtends angles at points P and Q on the minor and major arcs, respectively.

Draw a diameter BT and join A to T.

The aim is to prove thatAPBˆ =ABRˆ andAQBˆ =ABSˆ.

First prove thatAQBˆ =ABSˆ as this result is neededto prove thatAPBˆ =ABRˆ.