MHB How to Construct a Segment of Length $\dfrac {1}{a^3}+\dfrac {1}{b^3}$?

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given :AB=1 and ,CD=a, EF=b

Can you construct a segment with length =$\dfrac {1}{a^3}+\dfrac {1}{b^3}$
 
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Albert said:
given :AB=1 and ,CD=a, EF=b

Can you construct a segment with length =$\dfrac {1}{a^3}+\dfrac {1}{b^3}$
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Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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