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Serbia National Math Olympiad
2021 Serbia National Math Olympiad
3
3
Part of
2021 Serbia National Math Olympiad
Problems
(1)
Angle inequality
Source: Serbian Mathematical Olympiad 2021, P3
5/14/2021
In a triangle
A
B
C
ABC
A
BC
, let
A
B
AB
A
B
be the shortest side. Points
X
X
X
and
Y
Y
Y
are given on the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
such that
C
X
=
A
X
+
B
X
CX=AX+BX
CX
=
A
X
+
BX
and
C
Y
=
A
Y
+
B
Y
CY=AY+BY
C
Y
=
A
Y
+
B
Y
. Prove that
∡
X
C
Y
<
6
0
o
\measuredangle XCY<60^{o}
∡
XC
Y
<
6
0
o
.
geometry
geometrical inequality
inequalities