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3
Obtuse Triangle with Altitude
Obtuse Triangle with Altitude
Source: 2010 IrMO Paper 2 Problem 3
January 30, 2018
geometry
Problem Statement
In triangle
A
B
C
ABC
A
BC
we have
∣
A
B
∣
=
1
|AB|=1
∣
A
B
∣
=
1
and
∠
A
B
C
=
12
0
∘
.
\angle ABC=120^\circ.
∠
A
BC
=
12
0
∘
.
The perpendicular line to
A
B
AB
A
B
at
B
B
B
meets
A
C
AC
A
C
at
D
D
D
such that
∣
D
C
∣
=
1
|DC|=1
∣
D
C
∣
=
1
. Find the length of
A
D
AD
A
D
.
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