MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2016 Sharygin Geometry Olympiad
P13
P13
Part of
2016 Sharygin Geometry Olympiad
Problems
(1)
Nice geometry
Source:
1/9/2017
L
L
L
is a Line that intersect with the side
A
B
,
B
C
,
A
C
AB,BC,AC
A
B
,
BC
,
A
C
of triangle
A
B
C
ABC
A
BC
at
F
,
D
,
E
F,D,E
F
,
D
,
E
The line perpendicular to
B
C
BC
BC
from
D
D
D
intersect
A
B
,
A
C
AB,AC
A
B
,
A
C
at
A
1
,
A
2
A_{1},A_{2}
A
1
,
A
2
respectively Name
B
1
,
B
2
,
C
1
,
C
2
B_{1},B_{2},C_{1},C_{2}
B
1
,
B
2
,
C
1
,
C
2
similarly Prove that the circumcenters of
A
A
1
A
2
,
B
B
1
B
2
,
C
C
1
C
2
AA_{1}A_{2},BB_{1}B_{2},CC_{1}C_{2}
A
A
1
A
2
,
B
B
1
B
2
,
C
C
1
C
2
are collinear
geometry
circumcircle