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International Contests
Caucasus Mathematical Olympiad
2022 Caucasus Mathematical Olympiad
4
4
Part of
2022 Caucasus Mathematical Olympiad
Problems
(1)
Intersection point on circle
Source: VII Caucasus Olympiad, Senior, Day1 P4.
3/13/2022
Let
ω
\omega
ω
is tangent to the sides of an acute angle with vertex
A
A
A
at points
B
B
B
and
C
C
C
. Let
D
D
D
be an arbitrary point onn the major arc
B
C
BC
BC
of the circle
ω
\omega
ω
. Points
E
E
E
and
F
F
F
are chosen inside the angle
D
A
C
DAC
D
A
C
so that quadrilaterals
A
B
D
F
ABDF
A
B
D
F
and
A
C
E
D
ACED
A
CE
D
are inscribed and the points
A
,
E
,
F
A,E,F
A
,
E
,
F
lie on the same straight line. Prove that lines
B
E
BE
BE
and
C
F
CF
CF
intersectat
ω
\omega
ω
.
geometry