Let a circular metallic plate have a chord that subtends a right angle at the centre

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

Problem

Let a circular metallic plate have a chord that subtends a right angle at the centre. Using π=227\pi = \dfrac{22}{7}, answer the following. (i) Prove that the area AA (in cm2\text{cm}^2) of the segment cut off by a 90∘90^\circ chord in a circle of radius r cmr\,\text{cm} is given by A=2r27A = \dfrac{2r^{2}}{7}. (ii) The area of such a segment is 184.5 m2184.5\,\text{m}^2. Calculate the radius of the circle, correct to one decimal place. (iii) For the radius obtained in part (ii), determine the perimeter of the segment (sum of arc length and chord length) correct to the nearest centimetre.

Related theory

Browse the problem library