It is known that OC divides AOB into two parts and the following equation holds: (1) ∠ AOC = 1 / 3 right angle + 1 / 3 BOC (1) ∠ BOC = 1 / 3 flat angle - 1 / 3 AOC Question: (1) What is the location relationship between OA and ob? (2) Is OC the bisector of ∠ AOB? And write the judgment reason. (required) (self drawing) Be sure to write reasoning

It is known that OC divides AOB into two parts and the following equation holds: (1) ∠ AOC = 1 / 3 right angle + 1 / 3 BOC (1) ∠ BOC = 1 / 3 flat angle - 1 / 3 AOC Question: (1) What is the location relationship between OA and ob? (2) Is OC the bisector of ∠ AOB? And write the judgment reason. (required) (self drawing) Be sure to write reasoning

Question:
(1) What is the location relationship between OA and ob?
From the latter to the former, it is obtained that ∠ BOC - ∠ AOC = 60-30-1 / 3 (∠ AOC + ∠ BOC) = 30-1 / 3 ∠ AOB
Add the two formulas to get ∠ AOB = 60 + 30 + 1 / 3 (∠ BOC - ∠ AOC). Substitute the above formula to get = 90 + 1 / 3 (30-1 / 3 ∠ AOB) = 90 + 10-1 / 9 ∠ AOB, 10 / 9 ∠ AOB = 100, ∠ AOB = 90
A: perpendicular to each other
(2) Is OC the bisector of ∠ AOB? And write the judgment reason. (required)
A: Yes
The assumption is not true because ∠ AOC ≠ BOC, then ∠ AOC + BOC = 60 + 30 + 1 / 3 (∠ BOC - ∠ AOC) = 90 + 1 / 3 (∠ BOC - ∠ AOC) ≠ 90