Problem 192

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Problem 192: (2005 AMC 12a, 16)

Three circles of radius $s$ are drawn in the first quadrant of the $xy$-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the $x$-axis, and the third is tangent to the first circle and the $y$-axis. A circle of radius $r > s$ is tangent to both axes and to the second and third circles. What is $r/s$?

$(\mathrm {A}) \ 5 \qquad (\mathrm {B}) \ 6 \qquad (\mathrm {C})\ 8 \qquad (\mathrm {D}) \ 9 \qquad (\mathrm {E})\ 10$

Solution

Exercise 192: Solution

Three circles are drawn in the first quadrant of the $xy$-plane. The first circle has radius $2s$ and is tangent to both axes. The other two circles each have radius $s$: the second is tangent to the first circle and the $x$-axis, and the third is tangent to the first circle and the $y$-axis. A circle of radius $r > 2s$ is tangent to both axes and to the second and third circles. What is $r/s$?

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