Circle Theorems (Gen. Maths?)

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Prove that the bisectors of the four interior angles of a quadrilateral form a cyclic quadrilateral.

I do not understand 

Bisectors are just lines, if it's just any quadrilateral then these lines could go anywhere?

Thanks

[dcc]

A bisector is a line, but more importantly, a bisector divides the object into two equal parts.

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I understand how bisectors work, but in this problem the notion of bisectors creating more quadrilaterals sounds a bit loony to me.

[dcc]

Draw a quadrilateral with a line coming out of the interior angles (at half of the angle, as they bisect the angle) and draw this line out.  Doing this for all four angles, you should achieve a new quadrilateral made out of these lines.

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That's all I get

[dcc]

There is a quadrilateral in the middle!

[bigtick]

Let the bisectors bisect the interior angles into a,a; b,b; c,c; d,d.
One of the interior angle of the centre quadrilateral is 180-(a+b), the opposite angle of the centre quad. is 180-(c+d).
Sum of the two angles = 360-(a+b+c+d)=360-180=180.
So the centre quad. is cyclic.

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Thanks!!!