B explain why oap opa and label them as angle x on

(b) Explain why ∠ = ∠ OAP OPA
and label them as angle x
your copy of the diagram.
on
(c) Explain why ∠ = ∠ OBP OPB
and label them as angle y
your copy of the diagram.
(d) Express ∠ APB in terms of
x and
on
y.
A
B
P
O
A
B
P
Q
1.4
J
N
O
K
M
L θ
β

MEP Pupil Text - Additional Material: Mathematical Proof
24
(e) Use the sum of the angles in a triangle to explain why ∠ = °- AOP 180 2
and ∠ = °- BOP 180 2 y
(f) Use the fact that ∠ AOP, ∠ ∠ BOP and AOB are angles at a point to show
that ∠ = + AOB 2 2 x y
(g) Combine parts (d) and (f) to prove that ∠ = × ∠ AOB APB 2
11. O is the centre of the circle in the
diagram opposite.
M is the midpoint of the chord GH.
Prove that OM is perpendicular to GH.
( Hint : Join O to G, H and M.)
O
x
.
.
.
1.4
G H
M