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239 Open Math Olympiad
2017 239 Open Mathematical Olympiad
5
geometry with length condition \sqrt{2}(BC_BA)=AC
geometry with length condition \sqrt{2}(BC_BA)=AC
Source: 239 2017 J5
June 3, 2020
geometry
Problem Statement
Given a quadrilateral
A
B
C
D
ABCD
A
BC
D
in which
2
(
B
C
−
B
A
)
=
A
C
.
\sqrt{2}(BC-BA)=AC.
2
(
BC
−
B
A
)
=
A
C
.
Let
X
X
X
be the midpoint of
A
C
AC
A
C
. Prove that
2
∠
B
X
D
=
∠
D
A
B
−
∠
D
C
B
.
2\angle BXD=\angle DAB - \angle DCB.
2∠
BX
D
=
∠
D
A
B
−
∠
D
CB
.
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