MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia Regional
Indonesia Regional MO OSP SMA - geometry
2004.2
2004.2
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
AO/AD + BO/BE + CO / CF=2 wanted, cevians related
Source: 2004 Indonedia MO Province P2 q2 OSP
12/11/2020
Triangle
A
B
C
ABC
A
BC
is given. The points
D
,
E
D, E
D
,
E
, and
F
F
F
are located on the sides
B
C
,
C
A
BC, CA
BC
,
C
A
and
A
B
AB
A
B
respectively so that the lines
A
D
,
B
E
AD, BE
A
D
,
BE
and
C
F
CF
CF
intersect at point
O
O
O
. Prove that
A
O
A
D
+
B
O
B
E
+
C
O
C
F
=
2
\frac{AO}{AD} + \frac{BO}{BE} + \frac{CO}{ CF}=2
A
D
A
O
+
BE
BO
+
CF
CO
=
2
geometry
ratio
Cevians