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Sharygin Geometry Olympiad
2016 Sharygin Geometry Olympiad
P18
Sharygin 2016 (9-11)
Sharygin 2016 (9-11)
Source:
April 13, 2016
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
∠
C
=
9
0
∘
\angle C=90^{\circ}
∠
C
=
9
0
∘
, and
K
,
L
K, L
K
,
L
be the midpoints of the minor arcs AC and BC of its circumcircle. Segment
K
L
KL
K
L
meets
A
C
AC
A
C
,at point
N
N
N
. Find angle
N
I
C
NIC
N
I
C
where
I
I
I
is the incenter of
A
B
C
ABC
A
BC
.
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