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Mathematics
Mathematics
Problem
In quadrilateral
A
B
C
D
ABCD
A
B
C
D
,
A
B
=
A
D
AB = AD
A
B
=
A
D
and
C
B
=
C
D
CB = CD
C
B
=
C
D
. The diagonals
A
C
AC
A
C
and
B
D
BD
B
D
intersect at
O
O
O
. a. (i) Prove that
△
A
B
O
≅
△
A
D
O
\triangle ABO \cong \triangle ADO
△
A
B
O
≅
△
A
D
O
. b. (ii) Prove that
△
C
B
O
≅
△
C
D
O
\triangle CBO \cong \triangle CDO
△
C
B
O
≅
△
C
D
O
. c. (iii) Deduce that
O
B
OB
O
B
is perpendicular to
O
C
OC
O
C
.
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