MathDB
Problems
Contests
International Contests
Mediterranean Mathematics Olympiad
2013 Mediterranean Mathematics Olympiad
4
4
Part of
2013 Mediterranean Mathematics Olympiad
Problems
(1)
Two orthogonal circles
Source: MMC 2013
5/31/2013
A
B
C
D
ABCD
A
BC
D
is quadrilateral inscribed in a circle
Γ
\Gamma
Γ
.Lines
A
B
AB
A
B
and
C
D
CD
C
D
intersect at
E
E
E
and lines
A
D
AD
A
D
and
B
C
BC
BC
intersect at
F
F
F
. Prove that the circle with diameter
E
F
EF
EF
and circle
Γ
\Gamma
Γ
are orthogonal.
geometry proposed
geometry