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One of my beaded edge tyres recently came off the rim and I noticed it was quite rusty inside, are they safe?

The shape of the rim shares a high level of importance with the pressure, the nose at the tip of the clinch intrudes into the tyre forming a positive lock. However if this area is allowed to develop a sharp corroded edge it will rapidly cut the tyre bead. It is also common for restorers to cut this area back to provide a more sympathetic surface. This is a mistake and will lead to premature failure as it drastically reduces the support in this area.