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Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
1992 India Regional Mathematical Olympiad
4
4
Part of
1992 India Regional Mathematical Olympiad
Problems
(1)
A simple one on cyclic quads
Source: India RMO 1992 Problem 4
10/15/2005
A
B
C
D
ABCD
A
BC
D
is a cyclic quadrilateral with
A
C
⊥
B
D
AC \perp BD
A
C
⊥
B
D
;
A
C
AC
A
C
meets
B
D
BD
B
D
at
E
E
E
. Prove that
E
A
2
+
E
B
2
+
E
C
2
+
E
D
2
=
4
R
2
EA^2 + EB^2 + EC^2 + ED^2 = 4 R^2
E
A
2
+
E
B
2
+
E
C
2
+
E
D
2
=
4
R
2
where
R
R
R
is the radius of the circumscribing circle.
geometry
circumcircle
trigonometry
parallelogram
rectangle
cyclic quadrilateral
power of a point