The Geometry Question for the Day..

Given is the Square, ABDC with crosslines AD and BC

Within the square is an inscribed circle (purple)

At the intersection points of lines AD and BC and the circle is the square, EFHG.

within the square EFHG is an inscribed circle (orange)

At the intersection points of lines AD and BC and the (orange) circle is another square with two points, X and Y.

If the measurement of line AB is four inches, what is the measurement of line XY?

Be sure to show your work.

I majored in Math. That's why I have a job!

well la-de-freaking-dah for you, mathboy.

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Only if I'm right.

Which I'm quite sure I'm not. But it's up to Rodney to say so. Let's say it involved my less-than-perfect recollection of how to calculate chord lengths.

I never took geometry. My school didn't even offer it- they skipped us straight to pre-calc and Analysis.

It would be two inches, wouldn't it? 'Cause if you draw a line down the middle, it's obvious that half of the XY line is equal to one-fourth of the diameter of the largest square, and assuming that half of the XY line is one inch, one times four (since the one inch is equal to one-fourth the diameter) is (duh) four. So the XY line must be two inches long.

It's not Geometry, it's common sense.

Uh...do squares have diameters? The width, I guess. *shrugs*

I got 2 a really complicated way, using relationships of 45-45-90 triangles and diameters and similar triangles. But it also seems logical...I'll try to explain what I did, but then I'll feel really stupid if I'm wrong, so no judging...

Okay, so we know that the length of AB is 4, so if we multiply some number a by the square root of 2(by the 45-45-90 rules, or the pythagorean theorem), we get the length of AB, which is 4. This number a is 2.83. So the length of the segment QB is 2.83.

We can use similar triangles to say that the relationship between QB and AB is the same as the relationship between QF and EF. Therefore, the length of EF is 2.83.

So far we know:
AB=4
QB=2.83
QF=2
EF=2.83

Okay, so EF=diameter of the blue circle, so the line segment QY is half the length of EF. Therefore, QY is 1.41.

The relationship between QY and XY is the same as the relationship between QB and AB, so the length of XY is 2.

Hm...that was kind of fun...except that I wasted a lot of time I should have been doing my real homework that someone will grade...

I'll feel really stupid if I'm wrong now...

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Updated On: 10/19/04 at 07:44 PM

I love this!! post more so I can get to do them.

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And after 2 years of Calc in high school, I'm probably taking Statistics next year to fulfill my last natural sciences requirement. Urgh. I vowed to myself I'd never take math in college, but it's required for a political science major, so...

AHHH GEOMETRY!! *runs and hides*

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Hey, but BWYGUY2, if you know Math, you can calculate the probability of meeting ADAM FLEMING!!

I'm feeling better since NYBroadwayNY got the same answer the same way...I guess calculus didn't kill all my love for math. I really did like it at one point in my life...then came 3 semesters worth of calculus in two short semesters. Yeah, that was fun...

Plum--I like statistics! It makes sense to me, hopefully you'll enjoy it.

Back to the organic chem, which I definitely don't like.

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