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Baltic Way
2016 Baltic Way
17
Inequality in quadrilateral
Inequality in quadrilateral
Source: Baltic Way 2016, Problem 17
November 5, 2016
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral with
A
B
=
A
D
.
AB = AD.
A
B
=
A
D
.
Let
T
T
T
be a point on the diagonal
A
C
AC
A
C
such that
∠
A
B
T
+
∠
A
D
T
=
∠
B
C
D
.
\angle ABT + \angle ADT = \angle BCD.
∠
A
BT
+
∠
A
D
T
=
∠
BC
D
.
Prove that
A
T
+
A
C
≥
A
B
+
A
D
.
AT + AC \geq AB + AD.
A
T
+
A
C
≥
A
B
+
A
D
.
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