MHB What is the result of 6 divided by 2(1+2)?

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6 divided by 2(1+2)$$$$
 
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$\dfrac{6}{2(1+2)} = \dfrac{6}{2(3)} = \dfrac{6}{6} = 1$
 
This could also be done as $\frac{6}{2(1+ 2)}= \frac{6}{2}\frac{1}{3}= 3\left(\frac{1}{3}\right)= \frac{3}{3}= 1$.
 

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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