In order to derive the formula to calculate the angle at the centre of the sector, the formulae for the arc length and area of a sector can be rearranged so that we can calculate the fraction of ...
More simply, the angle at the centre is double the angle at the circumference. Angle OGK (\(x\)) = angle OKG because triangle GOK is also isosceles. Lengths OK and OG are also both radii. Angle GOH = ...
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