Let the radius of the inscribed circle be 2 units.
Calculating AB.
tanx = 2/a
a = 2/tanx
AB = 2+a
AB = 2+(2/tanx)
AB = (2tanx+2)/tanx
Calculating CD.
tanx = b/2
b = 2tanx
CD = 2+b
CD = 2+2tanx
It implies;
AB ÷ CD is;
((2tanx+2)/tanx)/(2+2tanx)
= (2tanx+2)/((tanx)(2tanx+2))
= 1/tanx
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