View source for 2018 UNCO Math Contest II Problems/Problem 5

== Problem ==
<asy>
filldraw(circle((2,0),1),white);
filldraw(circle((0,0),1),white);
filldraw(circle((-2,0),1),white);
draw((3,0)--(-1.75,sqrt(15)/4),black);
draw((3.5,0)--(-3.5,0),black);
pair A=(3,0),B=(.85,.4),C=(-.7,.75);
dot(A,black+0.25cm);dot(B,black+0.25cm);dot(C,black+0.25cm);
MP("A",A,NE);MP("B",B,N);MP("C",C,N);
</asy>

Find the length of segment BC formed in the middle circle by a line that goes through point A and is
tangent to the leftmost circle. The three circles in the
figure all have radius one and their centers lie on the
horizontal line. The leftmost and rightmost circles are
tangent to the circle in the middle. Point A is at
the rightmost intersection of the rightmost circle and the horizontal line.

== Solution ==

<math>\frac{8}{5}</math>

== See also ==
{{UNCO Math Contest box|year=2018|n=II|num-b=4|num-a=6}}

[[Category:Intermediate Geometry Problems]]