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Indonesia Regional
Indonesia Regional MO OSP SMA - geometry
2011.4
2011.4
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
EO _|_ ZD wanted, rectangle, equilateral, equal extensions related
Source: 2011 Indonesia MO Province P2 q4 OSP
12/10/2020
Given a rectangle
A
B
C
D
ABCD
A
BC
D
with
A
B
=
a
AB = a
A
B
=
a
and
B
C
=
b
BC = b
BC
=
b
. Point
O
O
O
is the intersection of the two diagonals. Extend the side of the
B
A
BA
B
A
so that
A
E
=
A
O
AE = AO
A
E
=
A
O
, also extend the diagonal of
B
D
BD
B
D
so that
B
Z
=
B
O
.
BZ = BO.
BZ
=
BO
.
Assume that triangle
E
Z
C
EZC
EZC
is equilateral. Prove that (i)
b
=
a
3
b = a\sqrt3
b
=
a
3
(ii)
E
O
EO
EO
is perpendicular to
Z
D
ZD
Z
D
geometry
rectangle