The parallelogram
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
has
![\angle BAD=A](/media/m/9/6/3/9637e9e23a3b749cf42bdabab00ca20f.png)
, and the triangle
![ABD](/media/m/a/5/4/a548bc577543629d304ecba1a042f910.png)
has all angles acute. Prove that circles radius
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
and center
![A,B,C,D](/media/m/8/5/d/85d135de173dbb765c7a2f175c5b2f60.png)
cover the parallelogram if and only
%V0
The parallelogram $ABCD$ has $AB=a,AD=1,$ $\angle BAD=A$, and the triangle $ABD$ has all angles acute. Prove that circles radius $1$ and center $A,B,C,D$ cover the parallelogram if and only
$$a\le\cos A+\sqrt3\sin A.$$