MathDB
Problems
Contests
International Contests
Silk Road
2008 Silk Road
2
2
Part of
2008 Silk Road
Problems
(1)
concurrent
Source:
8/30/2011
In a triangle
A
B
C
ABC
A
BC
A
0
A_0
A
0
,
B
0
B_0
B
0
and
C
0
C_0
C
0
are the midpoints of the sides
B
C
BC
BC
,
C
A
CA
C
A
and
A
B
AB
A
B
.
A
1
A_1
A
1
,
B
1
B_1
B
1
,
C
1
C_1
C
1
are the midpoints of the broken lines
B
A
C
,
C
A
B
,
A
B
C
BAC,CAB,ABC
B
A
C
,
C
A
B
,
A
BC
.Show that
A
0
A
1
,
B
0
B
1
,
C
0
C
1
A_0A_1,B_0B_1,C_0C_1
A
0
A
1
,
B
0
B
1
,
C
0
C
1
are concurrent.
geometry
circumcircle
incenter
angle bisector
geometry unsolved