'Open' the circle, safe space within

Hello!

I am making a game and I've got this problem. I want the circle to rotate and move toward my player, and my player has to stop in time to get into free space within the circle.

Here is the diagram just to show how it works.
https://www.dropbox.com/s/493jb3f4jvbfzlp/example.jpg

Touching black space is killing the player.

Any idea how to achieve it?

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