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Kürschák Math Competition
2012 Kurschak Competition
1
1
Part of
2012 Kurschak Competition
Problems
(1)
Angles and excenters
Source: Kürschák 2012, problem 1
7/4/2015
Let
J
A
J_A
J
A
and
J
B
J_B
J
B
be the
A
A
A
-excenter and
B
B
B
-excenter of
△
A
B
C
\triangle ABC
△
A
BC
. Consider a chord
P
Q
‾
\overline{PQ}
PQ
of circle
A
B
C
ABC
A
BC
which is parallel to
A
B
AB
A
B
and intersects segments
A
C
‾
\overline{AC}
A
C
and
B
C
‾
\overline{BC}
BC
. If lines
A
B
AB
A
B
and
C
P
CP
CP
intersect at
R
R
R
, prove that
∠
J
A
Q
J
B
+
∠
J
A
R
J
B
=
18
0
∘
.
\angle J_AQJ_B+\angle J_ARJ_B=180^\circ.
∠
J
A
Q
J
B
+
∠
J
A
R
J
B
=
18
0
∘
.
geometry