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Greece Junior Math Olympiad
2003 Greece Junior Math Olympiad
3
3
Part of
2003 Greece Junior Math Olympiad
Problems
(1)
rhombus wanted, starting with an isosceles (Greece Junior 2003)
Source:
7/12/2019
Let
A
B
C
ABC
A
BC
be an isosceles triangle (
A
B
=
A
C
AB=AC
A
B
=
A
C
). The altitude
A
H
AH
A
H
and the perpendiculare bisector
(
e
)
(e)
(
e
)
of side
A
B
AB
A
B
intersect at point
M
M
M
. The perpendicular on line
(
e
)
(e)
(
e
)
passing through
M
M
M
intersects
B
C
BC
BC
at point
D
D
D
. If the circumscribed circle of the triangle
B
M
D
BMD
BM
D
intersects line
(
e
)
(e)
(
e
)
at point
S
S
S
, the prove that: a)
B
S
/
/
A
M
BS // AM
BS
//
A
M
. b) quadrilateral
A
M
B
S
AMBS
A
MBS
is rhombus.
geometry
rhombus
isosceles