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Greece National Olympiad
2016 Greece National Olympiad
3
Greek contest 2016
Greek contest 2016
Source:
March 3, 2016
geometry
Problem Statement
A
B
C
ABC
A
BC
is an acute isosceles triangle
(
A
B
=
A
C
)
(AB=AC)
(
A
B
=
A
C
)
and
C
D
CD
C
D
one altitude. Circle
C
2
(
C
,
C
D
)
C_2(C,CD)
C
2
(
C
,
C
D
)
meets
A
C
AC
A
C
at
K
K
K
,
A
C
AC
A
C
produced at
Z
Z
Z
and circle
C
1
(
B
,
B
D
)
C_1(B, BD)
C
1
(
B
,
B
D
)
at
E
E
E
.
D
Z
DZ
D
Z
meets circle
(
C
1
)
(C_1)
(
C
1
)
at
M
M
M
. Show that: a)
Z
D
E
^
=
4
5
0
\widehat{ZDE}=45^0
Z
D
E
=
4
5
0
b) Points
E
,
M
,
K
E, M, K
E
,
M
,
K
lie on a line. c)
B
M
/
/
E
C
BM//EC
BM
//
EC
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