Okay, I can't get every detail down before class starts, but I'll put down a few basics. I'll insert intermediate steps later if needed.
Given: Three tangential, co-planar circles where no circle is inside another circle with radii $ a,b,c $
Find: Area of the triangle formed by connecting the centers of the circles with line segments.
Many of you will recognize this problem from ENGR 195 CHIPS Homework 5.2 Problem 3. Only, then you were given the actual lengths of the radii.
According to my calculations, if A is the area of the triangle, then:
$ A=\sqrt{abc(a+b+c)} $
I'm not going to show the proof right now so you all can have a chance to mess with it as well. I'll just say that I used the law of cosines to find the cosine of one angle, then the cosine function to find the length of the base of a right triangle with the same angle along the base, and then Pythagoreans theorem to find the height of the triangle, and finally the formula for the area of a triangle to find the area.
