Mathematics

Problem

A circle has radius

10\,\text{cm}

. A chord of the circle is

10\sqrt{3}\,\text{cm}

long. Solve the following. a. (i) Prove that the chord subtends an angle of

120^{\circ}

at the centre. b. (ii) Find, in exact form, the area of the corresponding minor segment, leaving your answer in terms of

\pi

and

\sqrt{3}

. c. (iii) Hence determine the area of the major segment of the circle.