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Sep 23, 2015 at 8:14 comment added asv It seems you are right, although I failed to see the relation to the above mentioned reference. Thank you.
Sep 23, 2015 at 8:13 vote accept asv
Sep 21, 2015 at 11:04 comment added Anton Petrunin @sva $\mu/100$ should work, do it more carefully better assume $K=0$ for beginning. You should get that $\alpha<\mathrm{const}\cdot\varepsilon$. The estimates are very close the proof of 7.16 in" A.D. Alexandrov spaces with curvature bounded below" by Burago, Gromov and Perelman.
Sep 21, 2015 at 8:55 comment added asv Following the nice idea you described, I tried to reconstruct the details. I got that the statement is true for triangles of diameter $\leq \varepsilon\mu/100$ rather than $\leq \mu/100$. Did I miss something or this is what you ment?
Sep 21, 2015 at 8:36 vote accept asv
Sep 21, 2015 at 8:51
Sep 21, 2015 at 8:36 history edited asv CC BY-SA 3.0
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Sep 20, 2015 at 17:23 history answered Anton Petrunin CC BY-SA 3.0