Explanation

From bc+cd = 2bd, dividing by bcd gives 1/d + 1/b = 2/c. With b = (a+c)/2 from a+c = 2b, substitution yields c(a+c+2d) = 2d(a+c), i.e. ac+c² = 2ad. Since a+c = 2b, this is 2bc = 2ad, so ad−bc = 0. The keyed option is C.