(1)△ABC is an equilateral triangle.

Prove:

∠∠ABC =∠APC = 60，∠BAC=∠CPB=60，

△ ABC is an equilateral triangle.

(2) When the point P is located at the midpoint of AB, the quadrilateral PBOA is a diamond.

Connect OP,

∠∠AOB = 2∠ACB = 120。

P is the midpoint of AB,

∴∠AOP=∠BOP=60

OA = OP = OB，

∴△OAP and△ △OBP are equilateral triangles.

∴OA=AP=OB=PB，

The quadrilateral PBOA is a diamond.