Simple Maths but can't crack it

Questions
1

Hi All,
very simple problem - I need to use a circle with 8 equi-spaced small circles just inside the circle circumference to act as buttons. I need to detect the touch of each circle to be able to decide. between 8 options. Read a lot of maths tries atan() and atan2() and a few other options but the solution keeps eluding me. I was trying with two vector centre to vertical radius and centre to inner circle centre.

The circles are effectively 45deg spaced and ideally I was hoping to convert positional calcs to the integers 1 to 8 to get a selection result. Any ideas?

2

@Bri_G Here’s a start.

viewer.mode=FULLSCREEN

function setup()
    a=""
end

function draw()
    background(0)
    stroke(255)
    strokeWidth(2)
    for z=0,359,45 do
        x=math.cos(math.rad(z))*100
        y=math.sin(math.rad(z))*100
        noFill()
        ellipse(x+WIDTH/2,y+HEIGHT/2,60)
        fill(255)
        text(z//45+1,x+WIDTH/2,y+HEIGHT/2)
    end 
    if a~="" then
        fill(255)
        text(a//45+1,WIDTH/2,HEIGHT/2)
    end
end

function touched(t)
    for z=0,359,45 do
        x=math.cos(math.rad(z))*100+WIDTH/2
        y=math.sin(math.rad(z))*100+HEIGHT/2
        if t.x>x-30 and t.x<x+30 and t.y>y-30 and t.y<y+30 then
            a=z
        end
    end    
end
3

Here’s a simple class version.

viewer.mode=FULLSCREEN

function setup()
    b1=button(400,200,80)
    b2=button(500,500,60)
end

function draw()
    background(0)
    b1:draw()
    b2:draw()
end

function touched(t)
    b1:touched(t)
    b2:touched(t)
end

button=class()

function button:init(x,y,s)
    self.x=x
    self.y=y
    self.size=s 
    self.val=0 
end

function button:draw()
    stroke(255)
    strokeWidth(2)
    fill(175, 224, 201)
    ellipse(self.x,self.y,self.size*3)
    for z=0,359,45 do
        local x=math.cos(math.rad(z))*self.size
        local y=math.sin(math.rad(z))*self.size
        fill(137, 234, 72)
        ellipse(x+self.x,y+self.y,self.size*.7)
        fill(255, 0, 0)
        text(z//45+1,x+self.x,y+self.y)
    end
    if self.val>0 then
        fill(255)
        text(self.val,self.x,self.y)
    end
end

function button:touched(t)
    if t.state==BEGAN then
        for z=0,359,45 do
            local x=math.cos(math.rad(z))*self.size+self.x
            local y=math.sin(math.rad(z))*self.size+self.y
            if t.x>x-self.size/2 and t.x<x+self.size/2 and t.y>y-self.size/2 and t.y<y+self.size/2 then
                self.val=z//45+1
            end
        end
    end
end
4

@dave1707 - thanks for both, gave me the pointer I needed. Will be posting results later.
Thanks again.