MathDB

Geometric locus problem about a constant sum

Source: Turkish NMO 1998, 5. Problem

July 31, 2011

geometrygeometric transformationreflectionparallelogramangle bisectorgeometry proposedHjelmslev

Problem Statement

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]