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India Contests
Regional Mathematical Olympiad
2002 India Regional Mathematical Olympiad
1
Altitudes
Altitudes
Source: Indian RMO 2002 Problem 1
October 27, 2005
geometry
Problem Statement
In an acute triangle
A
B
C
ABC
A
BC
points
D
,
E
,
F
D,E,F
D
,
E
,
F
are located on the sides
B
C
,
C
A
,
A
B
BC,CA, AB
BC
,
C
A
,
A
B
such that
C
D
C
E
=
C
A
C
B
,
A
E
A
F
=
A
B
A
C
,
B
F
F
D
=
B
C
B
A
\frac{CD}{CE} = \frac{CA}{CB} , \frac{AE}{AF} = \frac{AB}{AC} , \frac{BF}{FD} = \frac{BC}{BA}
CE
C
D
=
CB
C
A
,
A
F
A
E
=
A
C
A
B
,
F
D
BF
=
B
A
BC
Prove that
A
D
,
B
E
,
C
F
AD,BE,CF
A
D
,
BE
,
CF
are altitudes of triangle
A
B
C
ABC
A
BC
.
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