The first question uses the central angle theorem to find the angle BOD= 120 degrees, and then uses the arc length formula to find the length of the bad arc BD.
Solution: (1) connects OB and OD, because the angle BE=AB= 120 degrees, so the angle BOD= 120 degrees. The detailed answer is here/exercise/math /79946 1 as shown in the figure.
(1) If the radius of circle O is 3 and the angle DAB= 120 degrees, find the length of bad arc BD;
(2) Verification: BF =1/2bd;
(3) Let G be the midpoint of BD, and explore: Is there a point P (different from point B) on the circle O that makes PG=PF? And explain the positional relationship between PB and AE.