2006 AMC 12A Problems/Problem 17
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
?
Solution
One possibility is to use the coordinate plane, setting B at the origin. Point A will be (, 0) and E will be (
) since B, D, and E are collinear and contains the diagonal of ABCD. The Pythagorean theorem results in
This implies that and
; dividing gives us
See also
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Preceded by Problem 16 |
AMC 12A 2006 |
Followed by Problem 18 |
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