As shown in the figure, make the bisector ad of angle ∠ a of △ ABC, if AC + CD = AB, AC = BC, find the area of triangle ABC Under the condition of (1), extend ad to e, make ∠ DCE = CAD, prove that ad = 2ce

As shown in the figure, make the bisector ad of angle ∠ a of △ ABC, if AC + CD = AB, AC = BC, find the area of triangle ABC Under the condition of (1), extend ad to e, make ∠ DCE = CAD, prove that ad = 2ce

(1) obviously, from (AB-1) ^ 2 + (a-b) ^ 2 = 0, we can get: ab = 1 and A-B = 0, thus a = b = 1, that is, AC = BC = 1, intercept AF = AC on AB, link DF, it is easy to prove that △ ACD ≌ △ AFD ≌ ACD = AFD, CD = FD ≌ BDF = b = BAC ∫ BDF ≌ CDF = 180 ≌ BAC ≌ CDF = 180 ≌