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Random Geometry Problems from Ukrainian Contests
Ukrainian From Tasks to Tasks - geometry
2016.8
2016.8
Part of
Ukrainian From Tasks to Tasks - geometry
Problems
(1)
area chasing, # related (2016 From Tasks to Tasks, p8 Ukr)
Source:
5/3/2021
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. It is known that
S
A
B
D
=
7
S_{ABD} = 7
S
A
B
D
=
7
,
S
B
C
D
=
5
S_{BCD}= 5
S
BC
D
=
5
and
S
A
B
C
=
3
S_{ABC}= 3
S
A
BC
=
3
. Inside the quadrilateral mark the point
X
X
X
so that
A
B
C
X
ABCX
A
BCX
is a parallelogram. Find
S
A
D
X
S_{ADX}
S
A
D
X
and
S
B
D
X
S_{BDX}
S
B
D
X
.
geometry
areas
area
parallelogram