2020 AMC 10A Problems/Problem 16
Contents
Problem
A point is chosen at random within the square in the coordinate plane whose vertices are and
. The probability that the point is within
units of a lattice point is
. (A point
is a lattice point if
and
are both integers.) What is
to the nearest tenth
Solution
We consider an individual one by one block.
If we draw a quarter of a circle from each corner, the area covered by the circles should be . Because of this, and the fact that there are four circles, we write
Solving for , we obtain
, where with
, we get
, and from here, we simplify and see that
~Crypthes
To be more rigorous, note that
otherwise clearly the probability is greater than
. Then the above solution works.
Video Solution
~IceMatrix
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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