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National and Regional Contests
India Contests
India National Olympiad
1997 India National Olympiad
1
1
Part of
1997 India National Olympiad
Problems
(1)
Parallelogram problem
Source: INMO 1997 Problem 1
10/6/2005
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram. Suppose a line passing through
C
C
C
and lying outside the parallelogram meets
A
B
AB
A
B
and
A
D
AD
A
D
produced at
E
E
E
and
F
F
F
respectively. Show that
A
C
2
+
C
E
⋅
C
F
=
A
B
⋅
A
E
+
A
D
⋅
A
F
.
AC^2 + CE \cdot CF = AB \cdot AE + AD \cdot AF .
A
C
2
+
CE
⋅
CF
=
A
B
⋅
A
E
+
A
D
⋅
A
F
.
geometry
parallelogram
trigonometry
circumcircle
geometry solved