# How big does a rectangle have to be so that while rotating it, another smaller rectangle behind it is never visible?

Imagine I'm drawing a rectangle (rectSmall) of the size 1280x720.

This rectangle is static and never changes its position, size, rotation, etc.

Now I want to draw another, bigger rectangle on top of it (rectBig) that is continuously rotating around its center.

If rectBig has the same size as rectSmall, rectSmall will naturally be partly visible behind rectBig while rectBig is rotating (unless rectBig's rotation angle is 0 or 360).

My question is: How big does rectBig have to be so that rectSmall is never visible behind rectBig?

(Sorry for my English :D)

• Where is the centre of each rectangle? Is the big rectangle rotating about "its [own] centre" or "[the small rectangle's] centre"? – Nij Oct 11 '16 at 8:34
• rotating around its own center – user377314 Oct 11 '16 at 8:37
• and the rectangles have the same center – user377314 Oct 11 '16 at 8:42

The diagonal of rectSmall must be the minimal side length of rectBig.

• @user377314: That is nice to hear :o) – String Oct 11 '16 at 8:45

If the big rectangle has same centre as small rectangle,then big rectangle with minimum area to completely cover(during rotation) the small rectangle will be a square. The length of side of this square is the diameter of circle circumscribing the smaller rectangle. If you draw it, it would be clearer to you.