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a segment of a circle has a 120 arc and a chord of 8in. find the area of the segment.

Our aim is to calculate the Radius so that to use the formula related to the area of a segment of a circle, that is: Aire of segment = Ф.R²/2

Let o be the center of the circle, AB the chord of 8 in subtending the arc f120°

Let OH be the altitude of triangle AOB. We know that a chord perpendicular to a radius bisects the chord in the middle. Hence AH = HB = 4 in

The triangle HOB is a semi equilateral triangle, so OH (facing 30°)=1/2 R.  Now Pythagoras: OB² = OH² + 4²==> R² = (R/2)² + 16
R² = R²/4 +16. Solve for R ==> R =8/√3

OB² = OH² +