MHB I with solutions to these maths questions please

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The discussion centers around a request for help with math questions. The forum encourages users to share their progress or initial thoughts to facilitate effective assistance. Members are advised to post one question at a time for clarity. This approach helps helpers understand where the user is struggling and avoid redundant suggestions. Engaging in this manner enhances the support provided to users seeking solutions.
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Hi
I would like solutions / help with the maths questions attached here.
Thanks a lot

Regards
Afkurma
 

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Hello afkurma and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far? One question at a time, please. :)
 

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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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