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I have three positions, with an $X$ and $Y$ value and a value that indicates the distance to of each of the individual points (not in the same measurement). So to clarify my question:

I have three $XY$-positions and three values indicating the distance to the point (not in the same measurement). The lower the value is, the closer it is to the point.

For example: Point $1(x:5,y:8,$strength$:43)$ Point $2(x:22,y:23,$strength$:21)$ Point $3(x:26,y:52,$strength$:132)$

I don't know if the values are actually usable/make sense as I made them up just now...

The main goal is to calculate a point in the "center" of the three points, though it can be outside

Picture to explain it further

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    Does bigger or lower *strength* indicate nearness to the center? – 2017-01-07
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    I don't understand. Are you trying to find a circle through three points, or what? – 2017-01-07
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    Do you mean the [centroid](https://en.wikipedia.org/wiki/Centroid) of the three points ? – 2017-01-07
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    I will add a picture... – 2017-01-07

1 Answers 1

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Weighted ( by reciprocal strength $s$) average for each vertex

$$ \bar{ x} = \dfrac {x_1 s_1 + x_2 s_2 +x_3 s_3}{s_1+s_2+s_3} $$

$$ \bar{ y} = \dfrac {y_1 s_1 + y_2 s_2 +y_3 s_3}{s_1+s_2+s_3} .$$

where $$ s_i= \dfrac{1}{Strength_i} $$