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Old Kyiv MO Geometry
Kyiv City MO 1984-93 - geometry
1989.7.3
1989.7.3
Part of
Kyiv City MO 1984-93 - geometry
Problems
(1)
triangle construction given 2 midpoints 1989 Kyiv City MO 7.3
Source:
7/17/2021
The student drew a triangle
A
B
C
ABC
A
BC
on the board, in which
A
B
>
B
C
AB>BC
A
B
>
BC
. On the side
A
B
AB
A
B
is taken point
D
D
D
such that
B
D
=
A
C
BD = AC
B
D
=
A
C
. Let points
E
E
E
and
F
F
F
be the midpoints of the segments
A
D
AD
A
D
and
B
C
BC
BC
respectively. Then the whole picture was erased, leaving only dots
E
E
E
and
F
F
F
. Restore triangle
A
B
C
ABC
A
BC
.
geometry
construction