MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAMO
1993 USAMO
2
2
Part of
1993 USAMO
Problems
(1)
Convex quad
Source: USAMO 1993
10/27/2005
Let
A
B
C
D
\, ABCD \,
A
BC
D
be a convex quadrilateral such that diagonals
A
C
\, AC \,
A
C
and
B
D
\, BD \,
B
D
intersect at right angles, and let
E
\, E \,
E
be their intersection. Prove that the reflections of
E
\, E \,
E
across
A
B
,
B
C
,
C
D
,
D
A
\, AB, \, BC, \, CD, \, DA \,
A
B
,
BC
,
C
D
,
D
A
are concyclic.
geometry
USAMO