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Balkan MO Shortlist
2014 Balkan MO Shortlist
G5
G5
Part of
2014 Balkan MO Shortlist
Problems
(1)
perpendicular segments
Source: Balkan MO 2014 G-5
6/10/2015
Let
A
B
C
D
ABCD
A
BC
D
be a trapezium inscribed in a circle
k
k
k
with diameter
A
B
AB
A
B
. A circle with center
B
B
B
and radius
B
E
BE
BE
,where
E
E
E
is the intersection point of the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
meets
k
k
k
at points
K
K
K
and
L
L
L
. If the line ,perpendicular to
B
D
BD
B
D
at
E
E
E
,intersects
C
D
CD
C
D
at
M
M
M
,prove that
K
M
⊥
D
L
KM\perp DL
K
M
⊥
D
L
.
geometry
trapezoid