A circle having an area of 452 square inches is cut into two segments by a chord, which is 6 inches from the center of the circle. Find the area of the bigger segment.

Answer 1

the radius of the circle is 12. So, the angle θ subtended by the chord is 2π/3.

The area of the smaller segment is

1/2 r^2 (θ-sinθ)

That should get you started.

Answer 2

A of smaller segment = .5r^2((theta in rad) - sin (theta in degrees))

theta = 2(arccos(6/12))
theta=120

A of larger segment = A of circle - A of smaller segment
A = 452 - 12^2((120pi/180) - sin120)/2
A = 363.557