As shown in the figure, BD is the diameter of ⊙ o, OA ⊥ ob, M is the point on the inferior arc AB, through point m as the tangent of ⊙ o, the extension line of OA at point P, MD and OA at point n. (1) verification: PM = PN; (2) if BD = 4, PA = 32ao, through point B as BC ∥ MP intersection ⊙ o at point C, the length of BC

As shown in the figure, BD is the diameter of ⊙ o, OA ⊥ ob, M is the point on the inferior arc AB, through point m as the tangent of ⊙ o, the extension line of OA at point P, MD and OA at point n. (1) verification: PM = PN; (2) if BD = 4, PA = 32ao, through point B as BC ∥ MP intersection ⊙ o at point C, the length of BC

(1) It is proved that connecting OM, ∵ MP is tangent line of circle, ∵ om ⊥ PM, ∵ OMD + DMP = 90 °, ∵ OA ⊥ ob, ∵ ond + ODM = 90 °, ∵ MNP = ∵ ond, ∵ ODM = ∵ OMD, ∵ DMP = ∵ MNP, ∵ PM = PN. (2) let BC intersect om with E, ∵ BD = 4, OA = ob = 12bd = 2, ∵ PA = 3, ∵ Po =