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E$\\tilde{g}$ecio$\\tilde{g}$lu and Kalantari \\cite{kal} have shown that given any $p \\in S$, by computing its farthest in $S$, say $q$, and in turn the farthest point of $q$, say $q'$, we have ${\\rm diam}(S) \\leq \\sqrt{3} d(q,q')$. Furthermore, iteratively replacing $p$ with an appropriately selected point on the line segment $pq$, in at most $t \\leq n$ additional iterations, the constant bound factor is improved to $c_*=\\sqrt{5-2\\sqrt{3}} \\approx 1.24$. Here we prove when $m=2$, $t=1$. 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