  A sequence of rational points on an algebraic planar curve is said to form an
$r$-geometric progression sequence if either the abscissae or the ordinates of
these points form a geometric progression sequence with ratio $r$. In this
work, we prove the existence of infinitely many rational numbers $r$ such that
for each $r$ there exist infinitely many $r$-geometric progression sequences on
the unit circle $x^2 + y^2 = 1$ of length at least $3$.
