Problem Solving - mensuration circles

Chord AC at a distance of 7 cm from the center of a circle subtends an angle of 120 degrees at the center. Find the area of major segment.

 Answer: 1232/3 + 49*root(3)

 Explanation:















In triangle OCD,
Angle (COD) = 60 degrees
Angle (OCD) = 30 degrees
Hence tan(OCD) = OD/CD
CD = 7*root(3)
Sin(OCD) = OD/OC
OC = 14
Hence AC = 14*root(3)
Area of triangle AOC = (1/2)*AC*OD
                                         = (1/2)*14*root(3)*7
                                         = 49*root(3)
Area of sector AOC(reflex angle) = (240/360)*pi*14*14
                                                                 = 1232/3
Area of major segment = Area of sector AOC(reflex) + Area of triangle AOC
                                             = 1232/3 + 49*root(3)