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Mathematics
Mathematics
Problem
In a circle with centre
O
O
O
, two chords
A
B
AB
A
B
and
C
D
CD
C
D
are drawn. The perpendiculars from
O
O
O
meet the chords at
M
M
M
and
N
N
N
respectively. a. (i) If
A
B
=
C
D
AB = CD
A
B
=
C
D
, explain why
O
M
=
O
N
OM = ON
O
M
=
O
N
. b. (ii) If
O
M
=
O
N
OM = ON
O
M
=
O
N
, explain why
A
B
=
C
D
AB = CD
A
B
=
C
D
. (Give clear reasons for each statement.)
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