So I was thinking of making some div2B/C level CP problems for my school contest and thought of this....

Here it goes....

Find the maximum number of squares of side length 'a' that can completely be inscribed in a circle of radius 'r' such that exactly one of the vertices of the square touches the circle and no 2 squares overlap each other. Note that all the squares have to be completely inside the circle.

I cant figure this out..ended up taking too many variables which I cant eliminate...any thoughts or hints ?

The figure will look something like this :

No way am using geogebra for this

Apologize for the sketchy figure though.