find the area of the segment

Question

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find the angle subtended at th center by the minor arc and hence find the area of segment if the chord of the circle is 10 and radius is also 10.

Answer 1

If the chord is the same length as the radius of the circle, then the triangle formed by the chord and the radii is equilateral and the angle of the minor arc is 60 degrees. 60 degrees is 1/6 of 360 degrees so the area of the minor sector is 1/6 the area of the circle=100(pi)/6=52.36 sq units.