一題中四圓的演繹幾何

OA = OB = OC = OD = radius of circle.
since arc AB = arc CD, therefore, angle AOB = angle COD, so the 2 triangles are congruent (SAS). Since the 2 triangles are congruent, AB = CD.

(a)
BO=CO
AO=DO
angle AOB= angle DOC
triangle ABO ~= triangle DCO (SAS)
(b)
AB=DC by part (a)