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We prove that tangent cones of Lipschitz normally embedded sets are Lipschitznormally embedded. We also extend to real subanalytic sets the notion ofreduced tangent cone and we show that subanalytic Lipschitz normally embeddedsets have reduced tangent cones. In particular, we get that Lipschitz normallyembedded complex analytic sets have reduced tangent cones.

Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann