# Contracting a geodesic on a space of curvature less than 1

I would like to ask for a reference to the following statement (hopefully correct):

Let $M$ be a manifold of sectional curvature at most $1$ and let $\gamma$ be a closed geodesic. Suppose that $\gamma$ is contractible. Then for any contraction of this geodesic at some point its length will be equal to $2\pi$.

It would be even better if there is a reference for the case when $M$ a locally $CAT(1)$ space (not necessarily manifold)

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The soulution, thanks to rbell : warwick.ac.uk/~masgak/abstracts/lco.html – Dmitri Jul 15 '10 at 23:39