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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
10.2
10.2
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Conditional geo with quadrilateral and external tamgents
Source: Sharygin 2022 Finals 10-11.2
8/2/2022
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. The common external tangents to circles
(
A
B
C
)
(ABC)
(
A
BC
)
and
(
A
C
D
)
(ACD)
(
A
C
D
)
meet at point
E
E
E
, the common external tangents to circles
(
A
B
D
)
(ABD)
(
A
B
D
)
and
(
B
C
D
)
(BCD)
(
BC
D
)
meet at point
F
F
F
. Let
F
F
F
lie on
A
C
AC
A
C
, prove that
E
E
E
lies on
B
D
BD
B
D
.
geometry