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Pleae ignore that all-over-the-place title.

 

We're back for another \(MATH\) \(CHALLENGE!\) (in LaTex) I've been experimenting with some of the other features of the... question-maker? Anyway, you can probably see that in my new post about Euler's formula. Anyway anyway, I should tell you the answer to the last one, eh?

\(wxy=10\)

\(wyz=5\)

\(wxz=45\)

\(xyz=12\)

Find \(w+x+y+z\)

 

SOLUTION:

 

Multiply all equations together to get ​\(w^3x^3y^3z^3=2^33^35^3\)

\(wxyz=30\)

Now, divide to get \(w={30\over xyz}\)

Oh, we know \(xyz\)! Substitute to get \(w={5\over2}\)

Repeat to get \(x = 6\)\(y={2\over3}\), and \(z=3\). Add, add, add, and we get

\(w+x+y+z=12{1\over6}\)! Many people got this one.

 

Great! Now for the new problem:

 

Given point \(P\) outside a circle, the shortest distance between \(P\) and the circle's perimeter is 4 units, and the longest distance is 16 units. Find the distance of \(P\) from its tangent.

 

I'm excited to see some answers to this...

Mathhemathh  Oct 16, 2017
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2+0 Answers

 #1
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Given point  P outside a circle, the shortest distance between  P and the circle's perimeter is 4 units, and the longest distance is 16 units. Find the distance of P from its tangent.

 

Huh       It is 4 units. Oh... you mean the tangent that has the point P on it. ....

 

I used this property.

 

 

 

\(4*16=d^2\\ 64=d^2\\ distance=8\; units\)

Melody  Oct 16, 2017
edited by Guest  Oct 16, 2017
 #2
avatar+302 
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Nice! Not how I did it, but nice. (I didn't know this theorem existed frown)

Mathhemathh  Oct 17, 2017

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