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# Math Challenge (again!) #lim_(x->0)(1/x) (or ∞)

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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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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
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Nice! Not how I did it, but nice. (I didn't know this theorem existed )

Mathhemathh  Oct 17, 2017

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