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Topic: prove that an angle inscribed in a semicircle must be a right angle
Replies: 3   Last Post: Jan 25, 2008 11:39 PM

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Ladnor Geissinger

Posts: 313
From: University of North Carolina at Chapel Hill
Registered: 12/4/04
Re: prove that an angle inscribed in a semicircle must be a right angle
Posted: Jan 25, 2008 11:39 PM
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Here is an interesting variant of that problem which is appropriate for any discussion of vector geometry.

Suppose A and B are any two different points in 2,3, or n-space. Let S be the locus of all points X such that
(X-A)#(X-B)= 0 , where Y#W is the inner (dot) product of Y and W. Explain why S is a sphere (circle) with the segment from A to B as a diametral line. Hint: complete the square.



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