Problem:
Two unit squares ,,
with centers M, N are situated in the plane so that
. Two sides of
are parallel to the line MN, and one of the diagonals of
lies on MN. Find the locus of the midpoint of XY as X, Y vary over the interior of
,
respectively.
(1997 Bulgarian mathematical olympiad)
Solution:
Introduce complex numbers with ,
. Then, the locus is the set of points of the form
, where
,
, and
,
. The result is an octagon with vertices
,
, and so on.
Ref: Complex Numbers from A to …Z by Titu Andreescu and Dorin Andrica.
Thanks Prof. Andreescu !
Nalin Pithwa