MathDB
Problems
Contests
Undergraduate contests
Putnam
1967 Putnam
B1
B1
Part of
1967 Putnam
Problems
(1)
Putnam 1967 B1
Source: Putnam 1967
5/14/2022
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a hexagon inscribed in a circle of radius
r
.
r.
r
.
Show that if
A
B
=
C
D
=
E
F
=
r
,
AB=CD=EF=r,
A
B
=
C
D
=
EF
=
r
,
then the midpoints of
B
C
,
D
E
BC, DE
BC
,
D
E
and
F
A
FA
F
A
are the vertices of an equilateral triangle.
Putnam
geometry
euclidean geometry
hexagon