Geometry problem
The diagram shows two circles each of radius
and a square.The side length of the square can be written as
where
and
are co-prime. Find
.
The answer is 7.
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Let the side of the square be x. Draw a larger diagram and see for yourself that we get a right triangle with sides that are 1, (1-x) & (1-x/2) so that 1=(1-x)²+(1-x/2)² which yields x = 2/5