1, using the projective theorem: 1, cd 2 = ad * bd =18 * 8 =144, CD = 12, ac 2 = ad * ab =/kloc-0.

2. Because ∠ APD = 60, ∠ APB+∠ CPD = 120.

Because of the equilateral triangle ABC, ∠ ABC = 60, so ∠ APB+∠ BAP = 120.

∠CPD=∠BAP

So △ABP is similar to△ △PCD.

Get: AB/PC=BP/CD,

Because BP= 1, CD=2/3, PC=BC- 1=AB- 1.

So AB/(AB- 1)= 1/(2/3)

Solution: AB=3

△△ABC side length is 3.