2018 UNCO Math Contest II Problems/Problem 5

Problem

[asy] pair A=(3,0),B=((6+sqrt(1536))/50,(144-sqrt(1536))/(50*sqrt(24))),C=((6-sqrt(1536))/50,(144+sqrt(1536))/(50*sqrt(24))),D=(-1.8,sqrt(24)/5); filldraw(circle((2,0),1),white); filldraw(circle((0,0),1),white); filldraw(circle((-2,0),1),white); draw(A--D,black); draw((3.5,0)--(-3.5,0),black);  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

$\frac{8}{5}$

See also

2018 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
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