Question

A chord of circle of radius 14cm makes a right angle at the centre. Find the areas of minor and major segments of the circle.

Answer 1

Radius (r) = 14cm

𝜃 = 90°

= OA = OB

Area of minor segment (ANB)

= (𝑎𝑟𝑒𝑎 𝑜𝑓 𝐴𝑁𝐵 𝑠𝑒𝑐𝑡𝑜𝑟) − (𝑎𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝑂𝐵)

=`theta/360^@× pir^2 −1/2`× 𝑂𝐴 × 𝑂𝐵

=`90/360×22/7× 14 × 14 −1/2× 14 × 14`

= 154 − 98 = 56𝑐𝑚²

Area of major segment (other than shaded)

= area of circle – area of segment ANB

= 𝜋𝑟² − 56

=`22/7`× 14 × 14 − 56

= 616 – 56

= 560 cm².