For a circle of radius

MATHEMATICS · Multi-part · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

For a circle of radius rr, a chord subtends an angle of 60° at the centre. (i) Prove that the exact area of the corresponding segment is πr26−3r24\dfrac{\pi r^{2}}{6} - \dfrac{\sqrt{3} r^{2}}{4}. (ii) Hence find the area of such a segment when r=12 cmr = 12\,\text{cm}, leaving your answer in simplified surd form.

Related theory

Browse the problem library