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Contests
National and Regional Contests
Italy Contests
ITAMO
2016 ITAMO
3
3
Part of
2016 ITAMO
Problems
(1)
Excircle-related intersection on Thales circle of BC
Source: ITAMO 2016, Problem 3
5/11/2016
Let
Γ
\Gamma
Γ
be the excircle of triangle
A
B
C
ABC
A
BC
opposite to the vertex
A
A
A
(namely, the circle tangent to
B
C
BC
BC
and to the prolongations of the sides
A
B
AB
A
B
and
A
C
AC
A
C
from the part
B
B
B
and
C
C
C
). Let
D
D
D
be the center of
Γ
\Gamma
Γ
and
E
E
E
,
F
F
F
, respectively, the points in which
Γ
\Gamma
Γ
touches the prolongations of
A
B
AB
A
B
and
A
C
AC
A
C
. Let
J
J
J
be the intersection between the segments
B
D
BD
B
D
and
E
F
EF
EF
.Prove that
∠
C
J
B
\angle CJB
∠
C
J
B
is a right angle.
geometry