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[Virex]

Yes, but x/x² for x-> ∞ tends to 0, although for x = ∞ that reads ∞/∞² = ∞/∞...

[Bauglir]

@Christes

No need for a picture, that makes sense. Curses.

[ILikePie]

AB and CD are two equal chords in a circle. They meet at point E outside of the circle (AE > AB...), how do I prove that BE = DE?

[Darvi]

Uh... prove that AC and BD are parallel. That should do the trick.

[ILikePie]

I can see that, but how do I prove they're parallel?

[Darvi]

I'm thinking about that.

Give me a few minutes.


Okay so I have an idea, but I have to prove something about trapezes which we didn't do in school. Gotta research that.

So we have the quadrilateral ABCD. AB and CD, two opposite edges, are of equal length. That makes ABCD an isosceles trapezium. That means that the other two edges, AC and BD, are parallel.

And because of the intercept theorem, AE and BE are of equal length. QED.

Please take note that I totally ignored the naming conventions for corners.

[Christes]

According to that linked article, an isosceles trapezium requires a line of symmetry.  Simply having opposite sides of the same length is not enough.  I don't see an easy way to produce one, but I could be wrong.  You should be able to prove the lines are parallel by fooling around with angles:

For the chords AB and CD, draw a line segment from the center O to the endpoints.  This gives two triangles (OAB and OCD), each of which has one of your chords as a base and a vertex at the center.  It is not hard to prove that these triangles are congruent, so all corresponding angles are congruent.

Now look at the quadrilateral that Darvi mentioned.  You can break it into three triangles - the two previously mentioned ones, and one that is produced in the same way on chord BD.  All of these are isosceles, and two are congruent.  That should be enough to prove that m∠ABD=m∠BDC and m∠BAC=m∠DCA

[Darvi]

Right. Forgot that part. The line of symmetry is the one going through the centre of the circle and the middle of the arc BC. Or BD. Frankly, I've forgotten which point is which.

[klingon13524]

Damn exponents and square roots... Why would I ever need to know this?

[Darvi]

One word: interest rates.

[klingon13524]

One word: interest rates.

That's two words Mr. hotshot mathematician. And what do exponents have to do with simple or compound interest?

[Virex]

One word: interest rates.

That's two words Mr. hotshot mathematician. And what do exponents have to do with simple or compound interest?

Say you've got 10.000 Zloties on an account and you get 1% interest. You can then calculate the amount of Zloties on your bank account after Y years via:
Z = 10.000*1.01^y

[klingon13524]

Never mind.

[Virex]

After the 10th year you'd have:


Z = 1.01* 1.01* 1.01* 1.01* 1.01* 1.01* 1.01* 1.01* 1.01*  1.01*10.000... Good luck with that.   

[Darvi]

One word: interest rates.

That's two words Mr. hotshot mathematician.

Congratulations, you got the joke.