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Diameter of Flying Saucer

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Date: 5/27/96 at 10:57:19
From: Anonymous
Subject: Diameters of Flying Saucers

Dear Dr. Math,  I need some help on a landscaping project...

We are constructing an oval racetrack in Atlanta, and while
excavating for the project, we ran across a large circular object
buried in the ground edgewise.  The portion that we have uncovered so
far measures 10 meters high by 30 meters across.  We have not dug down
far enough to get a measurement on the diameter of this saucer-like
object. But we need to know the diameter so that we can tell how far
down we have to dig to get it out of the ground.  We don't want to
spend too much time with this thing.  It is radioactive... Thanks!
```

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Date: 5/27/96 at 21:11:2
From: Doctor Ken
Subject: Re: Diameters of Flying Saucers

Hello!

The first thing you need to do is hire someone else with a yellow
plastic suit to do your digging for you - no telling how your children
will look with all that radioactivity leaking around.

So let's assume this flying saucer is indeed saucer-shaped (several of
the flying saucers I've unearthed have looked like they were going to
be saucer-shaped at first, but sometimes when I dug up the whole thing
there was actually a big nose cone sticking directly downward, like
the craft took a nose dive into the ground. I guess they haven't
figured out how to land on our planet yet - perhaps their planet is
softer!). I've made a picture of the saucer, and you can see it on the
web at:

With the parts labeled as I have them in my picture, you've measured
the length of AC (it's half of 30, which is 15) and BC (which is 10).
And you want to figure out the radius of the circle.  Well, notice
that DA and DB are both radii, so they have the same length.  You can
call that length R.

Now look at the green triangle, triangle ACD. It's a right triangle,
and the top leg has length 15. The hypotenuse has length R, and the
other leg has length R-10. Can you use the Pythagorean Theorem to
figure out R?

Good luck!  And if you find any non-Earth creatures inside, tell
them Doctor Ken says howdy.

-Doctor Ken,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Triangles and Other Polygons

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