diameter, path, method
径 centers on a direct, narrow route: a path or shortcut, and by extension the straight-line distance across a circle (diameter). The method sense follows from a direct way of doing something.
径 is the modern simplified form of 徑. The older form combines 彳 (step, go) with 巠, which likely contributed the sound and the idea of a direct path or water channel. The modern right side 圣 is a simplification.
The left side 彳 suggests movement, and the right side 圣 looks like a straight line with a cross mark. Picture a direct path marked by a cross, leading straight to the destination—a shortcut or diameter.
For ケイ, imagine walking a narrow path and coming to a gate shaped like the letter K: K -> ケイ, and the path leads straight through.
diameter
aperture; bore; calibre; caliber
radius
diameter
bore; inside diameter
path; lane
groin; inguinal region
major axis
ionic radius
clad(ding) diameter
core diameter (of a fiber)
Schwarzschild radius
Bohr radius
conjugate diameter pair; CDP
covalent radius
radius vector
semi-major axis
aperture ratio (inverse of the f-number); relative aperture
vignetting
radius of gyration