**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

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