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ITAMO
2017 ITAMO
1
1
Part of
2017 ITAMO
Problems
(1)
Italian MO 2017 P1
Source: Italian MO 2017 P1
5/6/2017
Let
a
a
a
and
b
b
b
be positive real numbers. Consider a regular hexagon of side
a
a
a
, and build externally on its sides six rectangles of sides
a
a
a
and
b
b
b
. The new twelve vertices lie on a circle. Now repeat the same construction, but this time exchanging the roles of
a
a
a
and
b
b
b
; namely; we start with a regular hexagon of side
b
b
b
and we build externally on its sides six rectangles of sides
a
a
a
and
b
b
b
. The new twelve vertices lie on another circle. Show that the two circles have the same radius.
geometry
rectangle