2011 AMC 10A Problems/Problem 20
Problem 20
Two points on the circumference of a circle of radius r are selected independently and at random. From each point a chord of length r is drawn in a clockwise direction. What is the probability that the two chords intersect?
Solution
Fix a point from which we draw a clockwise chord. In order for the clockwise chord from another point
to intersect that of point
,
and
must be no more than
units apart. By drawing the circle, we quickly see that
can be on
of the perimeter of the circle.
See Also
2011 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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