MathDB
Problems
Contests
National and Regional Contests
North Macedonia Contests
JBMO TST - Macedonia
2014 JBMO TST - Macedonia
4
4
Part of
2014 JBMO TST - Macedonia
Problems
(1)
Macedonian JBMO TST 2014, Problem 4
Source:
3/30/2015
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
E
E
E
is the intersection of
A
B
AB
A
B
and
C
D
CD
C
D
,
F
F
F
is the intersection of
A
D
AD
A
D
and
B
C
BC
BC
and
G
G
G
is the intersection of
A
C
AC
A
C
and
E
F
EF
EF
. Prove that the following two claims are equivalent:
(
i
)
(i)
(
i
)
B
D
BD
B
D
and
E
F
EF
EF
are parallel.
(
i
i
)
(ii)
(
ii
)
G
G
G
is the midpoint of
E
F
EF
EF
.
geometry