Construct a square PQRS such that lines PQ, QR, RS, and SP pass through given points A, B, C, and D respectively.

Discuss the configuration of the given points when the construction is not possible.

(In reply to Partial Solution by Praneeth)

Praneeth,
I personally have some instances whereby I can sketch, and I seriously mean "sketch" ways to address this.

I do have to reflect as many of my thoughts are outside the author's ask which is:
     "Construct a square...."
and I place the emphasis on "construct" as Bractals is looking for a "pencil-compass" geometric solution.

Now, how do I interpret "partial" in your subject header?  Is it saying that from your algebraic statements that you totally void ALL instances (including a point being on an extension)?

From my playing I have a sense that one might be able to generate an algebraic solution for all cases, whether the points A, B, C and D are within P, Q R and S as vertices, or as locations on extensions.

The problem then however is, can those "external" instances be created via Euclidian construction?

Posted by brianjn on 2008-05-30 08:08:42