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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
10.3
10.3
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
max no of points of a line, <AXC=1/2<BXC or <BXC =12<AXC
Source: Sharygin Finals 2022 10.3
10/26/2022
A line meets a segment
A
B
AB
A
B
at point
C
C
C
. Which is the maximal number of points
X
X
X
of this line such that one of angles
A
X
C
AXC
A
XC
and
B
X
C
BXC
BXC
is equlal to a half of the second one?
geometry
equal angles
combinatorial geometry