Four distinct circles
![C,C_1, C_2](/media/m/1/9/1/19146f2b6b9e0d244be75a1df640e071.png)
, C3 and a line L are given in the plane such that
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
and
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
are disjoint and each of the circles
![C_1, C_2, C_3](/media/m/6/6/0/660c87c9c0706937199cd83c7028470f.png)
touches the other two, as well as
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
and
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
. Assuming the radius of
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
to be
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
, determine the distance between its center and
%V0
Four distinct circles $C,C_1, C_2$, C3 and a line L are given in the plane such that $C$ and $L$ are disjoint and each of the circles $C_1, C_2, C_3$ touches the other two, as well as $C$ and $L$. Assuming the radius of $C$ to be $1$, determine the distance between its center and $L.$