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


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 nspace. Let S be the locus of all points X such that (XA)#(XB)= 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.

