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Found problems: 1

1998 Turkey MO (2nd round), 2
Tags: geometry , geometric transformation , parallelogram , angle bisector , hjelmslev , reflection
Variable points $M$ and $N$ are considered on the arms $\left[ OX \right.$ and $\left[ OY \right.$ , respectively, of an angle $XOY$ so that $\left| OM \right|+\left| ON \right|$ is constant. Determine the locus of the midpoint of $\left[ MN \right]$.