Given AB is diameter of circle with centre O
∠COB = θ
Area of segment cut off, by AC = (area of sector) – (area of ΔAOC)
∠AOC = 180 – θ [∠AOC and ∠BOC form linear pair]
In ΔAOC, drop a perpendicular AM, this bisects ∠AOC and side AC.
Now, In ΔAMO,
Area of segment by AC = 2 (Area of sector BDC)