Will the shape always go pointy?

Sorry about the rather weird title, but I’ve been looking at this for so long that I’m going a bit crazy, OK so the inner green part of the picture the tip was curved but as I’ve increased the size of the red and yellow lines the tip has become very pointy, is that what always happens with a curved shape like this? I realise this is probably a really stupid question and I am well prepared to be told that. It’s just you know when you look at something for so long without another opinion, you start to imagine stuff, thanks guys!

Each time you inline, you decrease the radius at the tip.
So Yes. It will get pointy.

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Thank you sir, I thought I was going insane!