证明:(1)∵PM是圆O的切线,NAB是圆O的割线,N是PM的中点, ∴MN2=PN2="NA·NB," ∴=, 又∵∠PNA=∠BNP, ∴△PNA∽△BNP, ∴∠APN=∠PBN, 即∠APM=∠PBA. ∵MC="BC," ∴∠MAC=∠BAC, ∴∠MAP=∠PAB, ∴△APM∽△ABP. (2)∵∠ACD=∠PBN, ∴∠ACD=∠PBN=∠APN,即∠PCD=∠CPM, ∴PM∥CD, ∵△APM∽△ABP,∴∠PMA=∠BPA, ∵PM是圆O的切线,∴∠PMA=∠MCP, ∴∠PMA=∠BPA=∠MCP,即∠MCP=∠DPC, ∴MC∥PD, ∴四边形PMCD是平行四边形. |