[Thales semicircle theorem](http://en.wikipedia.org/wiki/Thales%27_theorem) says that an angle inscribed in a semicircle is a right angle.

> ***Q1***. Does a cone with apex on a hemisphere and encompassing the circular base
have a solid angle independent of the position of the apex?

It appears it *might* be true, with solid angle $(2-\sqrt{2})\pi \approx 0.59 \pi$ steradians:
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![ConeSolidAngle][1]
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> ***Q2***. I am seeking a proof or reference for the generalization to $d$ dimensions.

I have not found a reference, which makes me wonder if the answer to Q1 might be *No*...


  [1]: https://i.sstatic.net/FepAS.jpg