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locus,(AM)^2+(AN)^2=2(AB)^2, AB=AC

Source: 1989 Greece MO Grade XI p2

September 7, 2024
geometryLocus

Problem Statement

Let MM be a point on side BCBC of isosceles ABCABC (AB=ACAB=AC) and let NN be a points on the extension of BCBC such that (AM)2+(AN)2=2(AB)2(AM)^2+(AN)^2=2(AB)^2. Find the locus of point NN when point MM moves on side BCBC.
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