Difference between revisions of "2018 UNCO Math Contest II Problems/Problem 5"

Revision as of 01:01, 28 February 2025

$\frac{8}{5}$

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-== 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 ==

2018 UNCO Math Contest II (Problems • Answer Key • Resources)
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