Ω = d (b + d cot β);

Ω/d = b + d cot β;

(2)

Ω/d2 = b/d + cot β.

(3)

From (1) and (2),

χ = Ω / d − d cot β + 2d / sin β.

This will be a minimum for

dχ / dd = Ω / d2 + cot β − 2 / sin β = 0,

or