Difference between revisions of "2005 AMC 12B Problems/Problem 14"
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Revision as of 10:41, 4 July 2013
Problem
A circle having center , with
, is tangent to the lines
,
and
. What is the radius of this circle?
Solution
Let be the radius of the circle. Draw the two radii that meet the points of tangency to the lines
. We can see that a square is formed by the origin, two tangency points, and the center of the circle. The side lengths of this square are
and the diagonal is
. The diagonal of a square is
times the side length. Therefore,
.
See also
2005 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.