side of a square
A square ABCD is inscribed in a circle of radius 'a'. Another circle is inscribed in ABCD and a square EFGH is inscribed in this circle. The side EF is equal to :
(1)
(2) a
(3) a
(4)
If your answer is (4), type as 4.
The answer is 3.
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1 solution
The original circle has radius a. So 1/2 of the side of the inscribed square = a/sqrt(2). This is also the radius of the circle inscribed in the square.. Then the side, b, of the next inscibed square is given by b^2 = (a/sqrt(2))^2 + (a/sqrt(2))^2 = (a^2)/2 + (a^2)/2 = a^2, so b = a.