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239 Open Math Olympiad
2013 239 Open Mathematical Olympiad
3
A point on the incircle
A point on the incircle
Source: 239 2013 S3
August 7, 2020
geometry
Problem Statement
Inside a regular triangle
A
B
C
ABC
A
BC
, points
X
X
X
and
Y
Y
Y
are chosen such that
∠
A
X
C
=
12
0
∘
\angle{AXC} = 120^{\circ}
∠
A
XC
=
12
0
∘
,
2
∠
X
A
C
+
∠
Y
B
C
=
9
0
∘
2\angle{XAC} + \angle{YBC} = 90^{\circ}
2∠
X
A
C
+
∠
Y
BC
=
9
0
∘
and
X
Y
=
Y
B
=
A
C
3
XY = YB = \frac{AC}{\sqrt{3}}
X
Y
=
Y
B
=
3
A
C
. Prove that point
Y
Y
Y
lies on the incircle of triangle
A
B
C
ABC
A
BC
.
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