Three circles of radius a are drawn on the surface of a sphere of radius r. Each pair of circles touches externally and the three circles all lie in one hemisphere. Find the radius of a circle on the surface of the sphere which touches all three circles.
The smaller the three circles are (a) relative to the sphere's radius, r, the closer it is to Euclidean space.
Also, the radii involved can be expressed in various systems, so one must be decided upon. Is the radius of any circle (a or the solution circle) the arc length from its epicenter (on the surface of the sphere) to its circumference? ... or the Euclidean distance from its center on its secant plane? ... or the Euclidean distance from the epicenter to the circumference along the secant line?

Posted by Charlie
on 20210128 06:55:14 