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MATHEMATICS
GRADE 12
2021 REVISION MATERIAL
EUCLIDEAN GEOMETRY
A collection of questions from previous
question papers (2018 to 2020).
Prepared by T Faya
I LOVE MATHS SERIES
BOOK 2
Take note: Coding of questions.
KZN J18 – KZN June 2018
KZN S18 – KZN Sept 2018
ECS18 – Eastern Cape Sept 2018
NM17 – National March 2017
And so on …………….
This booklet is divided into 4 SECTIONS.
- SECTION A – Questions on proofs of examinable theorems.
- SECTION B – Questions on mostly level 1 and 2 problems.
- SECTION C – Questions on mostly level 2 to 3 problems.
- SECTION D – Mostly level 3 to level 4 questions
Examinable theorems.
In the diagram O is the centre of the circle. Use the diagram to prove the theorem which states that if
OM ⟘ AB then AM = MB.
In the diagram below, O is the centre of the circle ABCD.
Prove the theorem that states that
o
D 180
B
B
B
A
C
D
O
O
B
A
M
O
SECTION A
ΔABC and ΔDEF with D
ˆ A
ˆ ; E
ˆ B
ˆ and F
ˆ C
ˆ are shown below.
Prove that:
EF
BC
DF
AC
DE
AB
F
A
B C
E
D
Mostly Level 1 and 2 Questions on:
- Calculating angles.
- Finding angles equal to a specific angle.
- Finding angles equal to a given variable (usually x ).
EC S
SECTION B
QUESTION 8 KZNS
8.1 In the diagram, ABCD is a cyclic quadrilateral in the circle centered at O. ED is a tangent to
the circle at D. Chord AB is produced to F. Radii OC and OD are drawn. DE 40
(^) A and
C 65
2
Determine, giving reasons, the size of each of the following angles:
2
D
8.1.2 BC
F (4)
- GP S
- MP S
- WCS
- NM1
- NJ
- NJ
- NN
- NN
- KZNM
- KZNJ
- ECS
QUESTION 8 FSS
DF is a tangent to the circle at E. EKHG is a cyclic quadrilateral. EF 35.
K
o
O is the centre of the circle. (^) OK EHandEK HK.
8.1 Determine, with reasons, the size of each of the following:
4
E
KH
E
G
ˆ (2)
1
O
8.2 It is further given that EH = 24 units. KM = 4 units and the radius of the circle
EKHG is x .Determine the value of x. (4)
[13]
●
D
E
G
O
K
H
1
2 3
4
2
3
M
1
F
