Hi

DB' = BD' = AB - AD' = b - a cos(2 alpha)

CD = DB' + B'C = DB' + BB' / tan(alpha) = DB' + DD' / tan(alpha)

CD = b - a cos(2 alpha) + a sin(2 alpha) / tan(alpha)

CD = b - a (2 cosē(alpha) - 1) + a 2 sin(alpha) cos(alpha) cos(alpha) / sin(alpha)

CD = a + b

Of course you have also to consider the case where D' lies at the right of B