Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2015. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.