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Azerbaijan Contests
Azerbaijan Senior National Olympiad
2016 Azerbaijan National Mathematical Olympiad
2
2
Part of
2016 Azerbaijan National Mathematical Olympiad
Problems
(1)
Geometry with 18 degree
Source: Azerbaijan NMO 2016. Senior P2
7/27/2023
On the extension of the hypotenuse
A
B
AB
A
B
of the right-angled triangle
A
B
C
ABC
A
BC
, the point
D
D
D
after the point B is marked so that
D
C
=
2
B
C
DC = 2BC
D
C
=
2
BC
. Let the point
H
H
H
be the foot of the altitude dropped from the vertex
C
C
C
. If the distance from the point
H
H
H
to the side
B
C
BC
BC
is equal to the length of the segment
H
A
HA
H
A
, prove that
∠
B
D
C
=
18
\angle BDC = 18
∠
B
D
C
=
18
.
geometry