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2018 Turkey MO (2nd Round)
4
4
Part of
2018 Turkey MO (2nd Round)
Problems
(1)
Geometric Inequality with Excircle
Source: Turkey National Mathematical Olympiad 2018
12/2/2018
In a triangle
A
B
C
ABC
A
BC
, the bisector of the angle
A
A
A
intersects the excircle that is tangential to side
[
B
C
]
[BC]
[
BC
]
at two points
D
D
D
and
E
E
E
such that
D
∈
[
A
E
]
D\in [AE]
D
∈
[
A
E
]
. Prove that,
∣
A
D
∣
∣
A
E
∣
≤
∣
B
C
∣
2
∣
D
E
∣
2
.
\frac{|AD|}{|AE|}\leq \frac{|BC|^2}{|DE|^2}.
∣
A
E
∣
∣
A
D
∣
≤
∣
D
E
∣
2
∣
BC
∣
2
.
geometric inequality
geometry
inequalities
geometry proposed