GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutions

<formalization> consCDL: Shape(BO,OE,EB), Shape(BE,EA,AB), Shape(OAB,BA), Shape(ED,DA,AE),Shape(ODA,AD),Shape(CO,OB,BC), Shape(OBC,CB), Shape(OCD,DE,EO,OC), Collinear(OEA), Collinear(BED), Cocircular(O,ABCD) imgCDL: Equal(LengthOfLine(AB), LengthOfLine(OA)) </formalization> <think>According to the problem, we know that AB = OA, and O is the center of circle O. It is common knowledge that both OA and OB are the radii of circle O. From this, we can conclude that triangle BOA is isosceles since OA = OB. Further analysis shows that triangle OAB is also isosceles, leading us to deduce that all three sides of triangle BOA are equal, making it equilateral. Based on the properties of an equilateral triangle, we know that ∠BOA = 60°. Since ∠BOA = ⌒OAB, we find that ⌒OAB = 60°. According to the property of arcs, the angle subtended by the same arc at the circumference is half of the angle at the center. Therefore, we can derive that ∠BDA = ⌒OAB / 2. Substituting the known value of ⌒OAB, we calculate that ∠BDA = 30°. Thus, we have completed the entire solving process. </think> <answer>30</answer> Analyze the input geometry image to extract consCDL and imgCDL, then answer the question. Question: As shown in the diagram, AB=OA, the center of ⊙O is O. Find the measure of ∠BDA.