How to calculate coordinates of 6 point of intersection between a circle and a equilateral triangle?

Question

I know of an equilateral triangle the center (cx,cy) and the radius (r) of a blue circle which circumscribed it.

If I draw a green circle of any radius (radius), assuming the circle is large enough to have this intersection, can I get the coordinates of the 6 intersection points (P1, P2, P3...)?

I'm looking for P5JS/processing but any other clue can help me...

Thank you in advance

Answer 1

Distance from the center to top point is r.
Distance from the center to the lowest triangle side is r/2 (median intersection point is center, they are divided in 1:2 ratio).
Horizontal distance from cx to p4 (and p5) is (Pythagoras' theorem)

dx = sqrt(radius^2 - r^2/4)

So coordinates of p4 and p5 are (relative to center)

p4x = dx
p4y = r/2
p5x = -dx
p5y = r/2

Other points might be calculated using rotation by 120 degrees

p2x = p4x*(-1/2) - p4y*(sqrt(3)/2)
p2y = p4x*(sqrt(3)/2) + p4y*(-1/2)

and so on.

And finally add cx,cy to get absolute coordinates