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Assam Mathematics Olympiad
2023 Assam Mathematics Olympiad
12
12
Part of
2023 Assam Mathematics Olympiad
Problems
(1)
Assam Mathematics Olympiad 2023 Category III Q12
Source:
9/11/2024
In quadrilateral
A
B
C
D
ABCD
A
BC
D
,
A
D
∣
∣
B
C
AD || BC
A
D
∣∣
BC
, diagonals
A
C
AC
A
C
and
B
D
BD
B
D
are perpendicular to each other,
X
X
X
and
Y
Y
Y
are mid-points of
A
B
AB
A
B
and
C
D
CD
C
D
respectively. Prove that
A
B
+
C
D
≥
A
D
+
B
C
AB + CD \geq AD + BC
A
B
+
C
D
≥
A
D
+
BC
.