P9: In  convex  quadrilateral ABCD, ∠A=  60◦, ∠C=  30◦,  and AB=AD.   Show  that AC2=BC2+CD2.

since the thing we are trying to prove is very similar to a Pythagorean a^2 + b^2 = c^2, I have tried constructing or adding in lines of length a perpendicular to the original segment of length b, where a and b are BC and CD and trying to show that the hypotenuse of that right triangle is the same length as AC through similar triangles or other methods. I don't really think this method is going anywhere.