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Moldova Team Selection Test
2000 Moldova Team Selection Test
6
6
Part of
2000 Moldova Team Selection Test
Problems
(1)
the squares that have $BC$ and $AD$ as diagonals also have a common vertex
Source: Moldova TST 2000
8/7/2023
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. Two squares are constructed such that
A
B
AB{}
A
B
and
C
D
CD{}
C
D
are their diagonals. Show that if these squares have a common vertex inside
A
B
C
D
ABCD
A
BC
D
, then the squares that have
B
C
BC{}
BC
and
A
D
AD{}
A
D
as diagonals also have a common vertex inside
A
B
C
D
ABCD
A
BC
D
.
geometry