Thread: Geometric construction

Suppose that satisfy:



i). Give a geometric construction to prove there exists a triangle in the Euclidean plane (that is with the usual metric) with sides of length equal to .

I'm not really sure if I got this, but I chose a 5,12,13 triangle. It satisfies the inequalities, but i'm not sure if they want a more general answer.

ii). What special thing happens in your construction if one of the inequalities becomes equality, say, ?

With equality (I chose b=c), we get and . The second inequality seems a bit redundant since .

I don't really see the special thing that happens. My 5,12,13 triangle still works!

It seems to me that you have to prove that a triangle exists for arbitrary a, b, and c (subject to the constraints). Maybe you can consider a line segment of length a and two circles whose centers are the ends of the segment and whose radiii are b and c. Then show that the circles intersect when the inequalities hold.