Difference between revisions of "2006 AMC 12A Problems/Problem 17"
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== Problem == | == Problem == | ||
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| + | Square <math>ABCD</math> has side length <math>s</math>, a circle centered at <math>E</math> has radius <math>r</math>, and <math>r</math> and <math>s</math> are both rational. The circle passes through <math>D</math>, and <math>D</math> lies on <math>\overline{BE}</math>. Point <math>F</math> lies on the circle, on the same side of <math>\overline{BE}</math> as <math>A</math>. Segment <math>AF</math> is tangent to the circle, and <math>AF=\sqrt{9+5\sqrt{2}}</math>. What is <math>r/s</math>? | ||
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| + | <math> \mathrm{(A) \ } \frac{1}{2}\qquad \mathrm{(B) \ } \frac{5}{9}\qquad \mathrm{(C) \ } \frac{3}{5}\qquad \mathrm{(D) \ } \frac{5}{3}\qquad \mathrm{(E) \ } \frac{9}{5}</math> | ||
== Solution == | == Solution == | ||
Revision as of 23:58, 10 July 2006
Problem
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Square 
has side length 
, a circle centered at 
has radius 
, and and are both rational. The circle passes through 
, and lies on 
. Point 
lies on the circle, on the same side of as 
. Segment 
is tangent to the circle, and 
. What is 
?
