How can I find the minimum and maximum areas of a triangle?

Question

I'll be using Maple to figure this out, but I can't quite figure out the process. I need to find the minimum and maximum areas of a triangle if two of its vertices are (2,-1,0) and (3,2,2) and its third vertex is on the curve r->=<1+cost,sint,0>, t between 0 and Pi. To find the area of the triangle, I know I use 1/2 the cross product of the 2 vectors formed by the known vertices, but how to minimize the area I get stuck. Can anyone give me a clue?

PS. I'm not looking for Maple Code, rather, I would like to figure out the process to do it by hand, then I'll do it in Maple :)

Answer 1

You could use the distance formula to find the length of each side of the triangle. Then use Hero's formula to find the area.
Find the derivative dA/dt, set = 0 to find value of t that gives you max or min.

Shouln't be too hard since your curve is cofined to the xy plane.