Analysis: ABD is a regular triangle, which provides conditions for rotation. The purpose of rotation is to concentrate A, B and CD in a triangle.

Solution: rotate Δ δDBC 60 counterclockwise around point D? , get delta deltaδDAE, connect EC, and then

CD = ED and ∠EDC = 60?

∴δedc is an equilateral triangle, and EC = CD.

And AE = BC, therefore, from EC≤AE+AC, we know that CD ≤ A+B.

If and only if the lines C, A and E***, the equal sign holds, CD is the largest.

At this time ∠DCB =∠DEC =∠DCE = 60? , and ∠ACB =∠DCB+∠DCE.

∴∠ACB = 120？ , CD is the largest, and the maximum value is a+B.

For reference only.