Tuesday Trivia

Good one

I have an answer that checks out on a couple of examples, but I don't know how to obfuscate it, except to say that it uses three of the four primary functions, and is both radical and square.

Re: Tuesday Trivia

If "A" is a rock, and "B" is a hard place then I'd say that "C" is trapped. T.

Most likely, but

Sounds like it is probably right. I will wait for awhile to give others a chance to try it. Here is another one that is similar to keep you busy while you are waiting ;-)

The three colored circles in the diagram above have radii of 1, 2, and 3, and each are tangent to the other two. A fourth interior circle is tangent to all three colored circles. What is the radius of the interior circle? For extra credit what is the radius of the exterior circle (not pictured) that is tangent to the three colored circles?

More?

My head still hurts from the last one. I'm going to save these two for airplane timekillers.

Re: Most likely, but

That was a theorem from the coordinate guy.

Re: Most likely, but

Now you're tempting me. If I work on this and don't get my real work done, will you and Dan assume responsibility? ;-)

Not me ;-)

Like mission improbable. Your mission if you choose to accept it.... But if you are captured we will disavow any knowledge of you ;-)

Solution

Hopefully, it has been long enough.

ab/(sqrt(a)+sqrt(b))^2

Look at the lines connecting the centers of the circles. Their lengths are a+c, b+c, and a+b. The vertical components of those lines are a-c, b-c, and a-b. Pythagorus gives us the horizontal components of those lines, and noting that the horizontal distance between the centers of A and B is equal to the sum of the horizontal distances from A to C and C to B. it is easy to set up an algebraic expression leading to the answer above.

Now wait just a doggone minute here...

...did you just use EASY and ALGEBRAIC EXPRESSION in the same sentence ??? You make my head hurt ! ;-))

;-)