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

Latest revision as of 01:13, 14 January 2019

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

$\frac{8}{5}$

2018 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All UNCO Math Contest Problems and Solutions

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

Latest revision as of 01:13, 14 January 2019

Problem

Solution

See also

@@ Line 1: / Line 1: @@
 == 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((3,0)--(-1.75,sqrt(15)/4),black);
+draw(A--D,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);