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I need help with a formula. I have two circles. One is bigger than the other. I know the X, Y and R of the bigger one, but only Y and R of the smaller one, and that X is bigger than the bigger circles X. I also know how much percentage of the smaller one should be overlapped by the bigger one.

For example: The bigger one always have X1 = 150, Y1 = 250 and and R1 = 150. This will never change.

The smaller one have X2 > X1, Y2 = 250 (fixed number), R2 > 0 and R2 < 150 and that the percentage that should be covered by the bigger circle is >= 0% and <= 100%.

Does anyone know a formula for calculating what the samller ones X2 have to be in order for, for example 40% of it to be covered by the bigger one? Example photo: how far should I move circle B to the left?

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    Just to clarify: when you say "40% covered", you mean "40% of the *area* of the *smaller* circle is contained within the bigger circle", yes? – 2017-02-23
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    Use some geometry. You just have to find area of the common region. Use inclusion-exclusion principle. – 2017-02-23
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    Corrent, John. 40% of the smaller one should be covered by the bigger one. – 2017-02-23
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    Please add a photo, if possible. – 2017-02-23

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First you need the formula to compute the intersecting area of two circle knowing their center and radius. You can do this by computing triangle and pie sections. I'll leave the calculus to you, here is how to do it visually :

Visual operation to do the sum

The green and red of the pie portion are centered on their respective circle centers, obviously. If you know the angle $\theta$ of the vertex of the pie portion at the center of a circle, then its area is $\frac{\theta}{2} \cdot R^2$

The blue quadrilaterals vertices correspond to the two circle intersection points and the two circle centers. Computing the area of the triangles may be tricky, however they're isosceles. You can for instance to compute the distance between the two intersection points and compute the distance between each circle and the line joining the two intersection points, and take half of their product.

Once you have that formula, you equate it to $\frac{2}{5}$ of the area of the smaller disk. The only unknown value will be the $x$ value of the small circle, you can solve the equation and find that value.

Note, since you're working with relative areas, you can work up to an homothetic transformation, i.e. assume $X = Y = 0$ (translation) and $R = 1$ (scale) for the bigger circle and that the $Y$ value of the smaller and bigger circle are equals (rotation). That should simplify your computations.