As shown in the figure, the quadrilateral ABCD is inscribed in ⊙ o, BD is the diameter of ⊙ o, AE ⊥ CD, perpendicular foot is e, Da bisection ⊙ BDE

As shown in the figure, the quadrilateral ABCD is inscribed in ⊙ o, BD is the diameter of ⊙ o, AE ⊥ CD, perpendicular foot is e, Da bisection ⊙ BDE

It is proved that connecting OA. ∵ quadrilateral ABCD is inscribed in ⊙ o, and ∵ point a is on ⊙ o. ∵ Da bisection ∵ BDE, ∵ EDA = ∵ ODA. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp

As shown in the figure, the quadrilateral ABCD is inscribed in ⊙ o, BD is the diameter of ⊙ o, AE ⊥ CD, the perpendicular foot is e, Da bisects ⊙ BDE. (1) prove that AE is the tangent of ⊙ o; (2) if ⊥ DBC = 30 ° de = 1cm, find the length of BD

(1) It is proved that: connecting OA, ∵ Da, bisecting ∵ BDE, ∵ BDA = - EDA. ∵ OA = OD, ∵ ODA = - oad, ∵ oad = - EDA, ∵ OA ∥ CE. ∵ AE ⊥ CE, ∵ AE ⊥ OA. ∵ AE is the tangent line of ⊙ O. (2) ∵ BD is the diameter, ∵ BCD = - bad = 90 °.