Two externally tangent circles, one with radius 4 and the other with radius 1, have a common external tangent. What is the radius of a circle that is tangent to the two circles and to the external tangent?

Question

anonymous · Answer

Don't understand the question, got a picture?

anonymous · Answer

Nope. All i have is the problem and the answer.
The answer is 4/9, but i need to know how to solve it.

anonymous · Answer

If I could draw it, I could help, but I can't draw it....

anonymous · Answer

okay. Thanks for trying...

anonymous · Answer

Seems everyone else has same problem:-)

When you say "externally tangent" and "common external tangent" do you mean that the 2 circles are touching?

anonymous · Answer

they touch at exactly one point and have a line that is tangent to both. they look like this

anonymous · Answer

Ok, got it, so you want the teeny little circle squished between the 2 circles and the external tangent, right?

anonymous · Answer

yeah. I think that's what it is asking

anonymous · Answer

K, let me take a look...

anonymous · Answer

thanks!

anonymous · Answer

1/sqrt(r) = 1/sqrt(4) + 1/sqrt(1) -> r = 4/9 http://en.wikipedia.org/wiki/Ford_circle

anonymous · Answer

thank you!!!