∵AB is the diameter⊙ O,

∴∠APB=90。

∴∠APC=90。

∫Q is the midpoint of communication

∴ PQ = AQ = QC。 ( 1)

∴∠PAQ=∠APQ

OA = OP，

∴∠OAP=∠OPA

∴∠PAQ+∠OAP=∠APQ+∠OPA

That is ∠OAQ=∠OPQ.

∫∠BAC = 90，

∴∠OPQ=90，

∴PQ⊥OP

∴PQ is tangent to⊙ O (2 points)

(2)∫PQ = 2

∴AC=4.

∠∠BAC = 90, AP⊥BC in P,

∴△ ACP ∽△ BCA。 (3 points)

∴ACBC=PCAC

∴AC2=PC？ B.C.

BP = 6，

∴ 16=PC(6+PC)

∴PC=2 (minus points) (4 points)

∴BC=8，

∴AB=82？ 42=43,

The radius of a circle is 23 cm. (5 points)