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Hi I'm sorry i'm coming to you because i'm really bad at maths. But i'm trying to create a visualisation for my project... My issue is that I want to make the 4 big circles grow proportionally when the green circle radius grow as well. Uhm i don't know if it's very clear ...

small green circle radius = 35

Bottow circle has radius = 135 , x = 0 , y = -100 ,
Top circle has radius = 135 , x = 0 , y = 100

Left circle has radius = 135 , x = -100 , y = 0 ,
Right circle has radius = 135 , x = 100 , y = 0

I would be very greatful of your help

IMAGE IMAGE

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    $\begingroup$ Try scaling all the values and coordinates by $k>1$: $\quad (x,y)\to(kx,ky)$ $\endgroup$
    – Alexey Burdin
    Commented Jun 28, 2020 at 0:13
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    $\begingroup$ Thank you Alexey ! $\endgroup$
    – Helena Rousseaux
    Commented Jun 28, 2020 at 0:23

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Let's say your green circle is: $$x^2+y^2=r^2$$

The radius of the bigger circles will be: $\frac{135r}{35}=\frac{27r}{7}$

Let's do the circle to the right of the green circle.

The centre of the circle to the right will be: $(x,y)=(\frac{20r}{7},0)$

The equation of the circle to the right will be: $$(x-\frac{20r}{7})^2+y^2=(\frac{27r}{7})^2$$

Graph that and see if it works. Whatever value you choose for $r$ the big circle should scale to it.

See if you can figure out the other circles.

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