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Mathematics
Mathematics
Problem
In a circle with centre
O
O
O
, let
A
B
AB
A
B
be a chord that is not a diameter. The midpoint of
A
B
AB
A
B
is
M
M
M
. The straight line
O
M
OM
O
M
meets the circle again at
C
C
C
on the major arc
A
B
AB
A
B
. (a) Prove that
∠
A
M
C
=
90
∘
\angle AMC = 90^{\circ}
∠
A
M
C
=
9
0
∘
. (b) Show that
A
C
=
C
B
AC=CB
A
C
=
C
B
.
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