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All-Russian Olympiad
1969 All Soviet Union Mathematical Olympiad
115
115
Part of
1969 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 115 All Soviet Union MO 1969 equal perimeters inside trapezoid
Source:
6/23/2019
The point
E
E
E
lies on the base
[
A
D
]
[AD]
[
A
D
]
of the trapezoid
A
B
C
D
ABCD
A
BC
D
. The perimeters of the triangles
A
B
E
,
B
C
E
ABE, BCE
A
BE
,
BCE
and
C
D
E
CDE
C
D
E
are equal. Prove that
∣
B
C
∣
=
∣
A
D
∣
/
2
|BC| = |AD|/2
∣
BC
∣
=
∣
A
D
∣/2
geometry
perimeter
trapezoid