Easy geometry

[grayfalcon89]

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.

[ydoaPs]

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.

[psi20]

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.

[grayfalcon89]

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.