Math Is Fun Forum

tacowreck

Member

Registered: 2016-02-27

Posts: 4

Help geo math problem

Each of the three circles in the figure below is externally tangent to the other two, and each side of the triangle is tangent to two of the circles. If each circle has radius three, then find the perimeter of the triangle.

[asy]
unitsize(0.5 cm);

draw(Circle(dir(90),sqrt(3)/2));
draw(Circle(dir(90 + 120),sqrt(3)/2));
draw(Circle(dir(90 + 240),sqrt(3)/2));
draw((1 + sqrt(3))*dir(90)--(1 + sqrt(3))*dir(90 + 120)--(1 + sqrt(3))*dir(90 + 240)--cycle);
[/asy]

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Help geo math problem

I am getting

Last edited by evene (2016-02-27 10:30:03)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help geo math problem

Too bad you did not use Geogebra.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,163

Re: Help geo math problem

hi tacowreck

Hope I've got this diagram right.

As DG = 3 and triangle ADG is 30-60-90, => AG = 3root(3).  HC = same by symmetry.

DGHF is a rectangle so GH = 3+3 = 6

So AC = 6root(3) + 6.

evene's answer follows from this.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Help geo math problem

Yeah. You're diagram is correct. I plotted the Asymptote commands and it looks exactly like yours.

Give or take some lines.

tacowreck

Member

Registered: 2016-02-27

Posts: 4

Re: Help geo math problem

Thank You. I got it