The above result may be obtained thus (fig. 116):--

[chi] = b + 2d/sin [beta]. (1)

[Omega] = d(b + d cot [beta]);

[Omega]/d = b + d cot [beta]; (2)

[Omega]/d² = b/d + cot [beta]. (3)

From (1) and (2),

[chi] = [Omega]/d - d cot [beta] + 2d/sin [beta].