There are two intersecting congruent circles, and I only know the length of the small arcs (coloured in red the image above), is there any way to find out the distance between the radii of the two circles? Thank you. :)
@amitava gave you the correct answer, for the general case of any 𝜃, r and 𝑙. In this specific case, since 𝜃 is 60° [𝜃/360°=2𝜋/3/4𝜋], we can solve it using basic geometry, without trigonometric functions.
All the radii are equal, so if you connect the centers with the endpoints of the arc, you get a rhombus. In a rhombus, the diagonals bisect the, bisect each other, and are perpendicular to each other.
You can see a detailed step-by-step proof here:https://geometryhelp.net/distance-between-centers-overlapping-congruent-circles/