Solid Geometry Mensuration - Circles | Wizako

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)

Solid Geometry Mensuration – Circles