Geometry Question

[Unoriginal Name]

At work today we were trying to figure out the following problem that a co-worker's sister had for homework the night before and I just couldn't remember how to do it and now it is bugging me. There is a right triangle with legs of 3 and 4. Inside the triangle are two circles. I believe the large circle touches the triangle in exactly three places and the smaller circle touches the triangle in only two places. The circles touch each other at exactly one place. Now the question is as follows: What are the radii of the two circles? I figured out the radius of the larger circle is 1. How do I figure out what the radius of the smaller circle is? I haven't had geometry in about 14 years so this stuff isn't fresh in my mind but at the same time it is bugging me how to figure it out.

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[youvalss]

Re: Geometry Question

Where do u work that u have time for solving geometry questions? I want to work there too
Sorry man, tried to solve it but then realized that I don't remember a thing in geometry.

[Cyros]

Re: Geometry Question

Hell, I don't even remember covering a question like that in high school geometry and it's only been about 5 years since I had it.

[Unoriginal Name]

Re: Geometry Question

Where do u work that u have time for solving geometry questions? I want to work there too
Sorry man, tried to solve it but then realized that I don't remember a thing in geometry.

Somebody posed the question at lunch because she couldn't figure it out.

[HiJumpr111]

Re: Geometry Question

I worked on this problem quite a bit today with another teacher friend of mine and this is what we got for the radius of the smaller circle....
It ain't pretty....

It would be the solution to the equation
4r^2+(2sqrt(5)-2)r-(6+2sqrt(5))=0
Since this is an ugly quadratic, I had to use a graphing calulator to solve and I got
r approximately = 0.381.

I, like you, got 1 for the radius of the larger circle.

I'll keep looking at this over the next day or so. It's a fairly common problem that I have seen before, but I could not remember its solution. It's definitley not for the faint of heart.

BTW, Good job on your answer for the big circle.

[superjames1992]

Re: Geometry Question

I had geometry one year ago and I don't even remember how to do that, LOL! Of course, I really didn't like geometry. Algebra, on the other hand, is a really cool subject.

[Sandman42]

Re: Geometry Question

I had geometry one year ago and I don't even remember how to do that, LOL! Of course, I really didn't like geometry. Algebra, on the other hand, is a really cool subject.

I bet you love the transitive property.