Take some point V and draw two rays from it. Choose some other point W in between those two rays. Then, construct a line that touches both rays and passes through W.

Now, this line forms a closed triangle together with the two rays. The point W divides this line into two segments (x1, x2). What is the ratio of these two segments such that the area of the enclosed triangle is minimal?

Does this minimal area even exist?

I set up three equations and was able to show that the ratio is indeed one using calculus ( I would rate the problem as D3 due to the messiness of this solution ).

An additional problem would be given the points V and W and the two rays, to construct the line using a straightedge and compass.

Posted by Bractals on 2010-03-30 06:07:48