I don't think any of the people in here are basic on math but here it goes the basic geometry proving:

 

Prove that if you construct a triangle from connecting the centers of the three congruent circles that are tangent to each other, you form an a equilateral triangle.

i have no clue on proofs(haven't done them since freshman year), but i may be able to give you an idea.

 

you have three circles:1,2, and 3

 

[math]r_1=r_2=r_3[/math]

 

each side of the triangle is 2r.

 

all sides are the same, therefore it is equilateral.

Basically, when you connect radiuses of the circles so that the radiuses are colinear, you get a leg of the triangle. Since the radii are equal (congruent circles), they form an equilateral triangle.

Good.. More mathy, it would be:

 

Let's call x = radius of circle A.

 

Since circle A, B, and C are congruent, they'll have same radius, x.

 

Each side, connecting AB, BC, and AC will have x+x, x+x, and x+x. Since x+x are for all three sides, they're equilateral, which we wanted to prove.