AB is the diameter of the circle O, Pb tangents the circle O to B, D on the circle O, ad ‖ Po, prove that PD is the tangent of the circle o

AB is the diameter of the circle O, Pb tangents the circle O to B, D on the circle O, ad ‖ Po, prove that PD is the tangent of the circle o

prove;
Connect OD
∵OA=OD
∴∠OAD=∠ODA
∵AD//PO
℅ ∠ oad = ∠ BOP [isoangle]
∠ ODA = ∠ DOP [internal stagger angle]
∴∠BOP=∠DOP
OB = OD, Op = op
∴⊿BOP≌⊿DOP(SAS)
∴∠PDO=∠PBO
∵ Pb is tangent to circle O, ∠ PbO = 90 & # 186;
∴∠PDO=90º
P D is the tangent of circle o