As shown in the figure, ⊙ o is the circumscribed circle of the quadrilateral ABCD, with the center o on ad, OC ∥ ab. (1) prove that AC bisects DAB; (2) if AC = 8, ad: BC = 5:3, try to find the radius of ⊙ o

As shown in the figure, ⊙ o is the circumscribed circle of the quadrilateral ABCD, with the center o on ad, OC ∥ ab. (1) prove that AC bisects DAB; (2) if AC = 8, ad: BC = 5:3, try to find the radius of ⊙ o

(1) It is proved that: ∵ OC ∥ ab ∥ OCA = ∥ BAC ∵ OA = OC ∥ OAC = ∥ OCA ∥ OAC = ∥ BAC is AC bisection DAB; (2) ∥ AC bisection DAB, ∥ arc CD = arc BC ∥ CD = BC and ad: BC = 5:3 ∥ ad: CD = 5:3 ∥ ad is the diameter of a circle, ∥ ACD = 90 ° according to the Pythagorean theorem, ad: CD: AC = 5:3:4, so ad = 10, that is the radius of a circle is 5