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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2006 Sharygin Geometry Olympiad
9
9
Part of
2006 Sharygin Geometry Olympiad
Problems
(1)
concurrency defined by angles and lines of unit circle
Source: Sharygin 2006 VIII-X CR 9
8/23/2019
L
(
a
)
L(a)
L
(
a
)
is the line connecting the points of the unit circle corresponding to the angles
a
a
a
and
π
−
2
a
\pi - 2a
π
−
2
a
. Prove that if
a
+
b
+
c
=
2
π
a + b + c = 2\pi
a
+
b
+
c
=
2
π
, then the lines
L
(
a
)
,
L
(
b
)
L (a), L (b)
L
(
a
)
,
L
(
b
)
and
L
(
c
)
L (c)
L
(
c
)
intersect at one point.
angles
geometry
circle
concurrent
concurrency