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We match sets M of points in the coordinate plane

Source: IMO LongList 1988, Vietnam 1, Problem 89 of ILL

November 9, 2005

analytic geometrygeometrygeometric transformationreflectiongeometry unsolved

Problem Statement

We match sets

M

of points in the coordinate plane to sets

M*

according to the rule that

(x*,y*) \in M*

if and only if x \cdot x* \plus{} y \cdot y* \leq 1 whenever

(x,y) \in M.

Find all triangles

Q

such that

Q*

is the reflection of

Q

in the origin.