MathDB
Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
1991 India Regional Mathematical Olympiad
5
5
Part of
1991 India Regional Mathematical Olympiad
Problems
(1)
Parallel lines
Source: India RMO 1991 Problem 5
10/15/2005
Take any point
P
1
P_1
P
1
on the side
B
C
BC
BC
of a triangle
A
B
C
ABC
A
BC
and draw the following chain of lines:
P
1
P
2
P_1P_2
P
1
P
2
parallel to
A
C
AC
A
C
;
P
2
P
3
P_2P_3
P
2
P
3
parallel to
B
C
BC
BC
;
P
3
P
4
P_3P_4
P
3
P
4
parallel to
A
B
AB
A
B
;
P
4
P
5
P_4P_5
P
4
P
5
parallel to
C
A
CA
C
A
; and
P
5
P
6
P_5P_6
P
5
P
6
parallel to
B
C
BC
BC
, Here,
P
2
,
P
5
P_2,P_5
P
2
,
P
5
lie on
A
B
AB
A
B
;
P
3
,
P
6
P_3,P_6
P
3
,
P
6
lie on
C
A
CA
C
A
and
P
4
P_4
P
4
on
B
C
BC
BC
> Show that
P
6
P
1
P_6P_1
P
6
P
1
is parallel to
A
B
AB
A
B
.
geometry
parallelogram