(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.