MathDB

Vietnam

Source: Vietnam MO 1991, #3, first day

March 22, 2006

geometry3D geometryspheregeometry unsolved

Problem Statement

Three mutually perpendicular rays

O_x,O_y,O_z

and three points

A,B,C

on

O_x,O_y,O_z

, respectively. A variable sphere є through

A, B,C

meets

O_x,O_y,O_z

again at

A', B',C'

, respectively. Let

M

and

M'

be the centroids of triangles

ABC

and

A'B'C'

. Find the locus of the midpoint of

MM'

.

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