2011 AMC 10A Problems/Problem 20
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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 you 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.