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

Question

Philoid · Accepted Answer

Radius of the circle = 14cm

Angle subtend at center = 90°

By Pythagoras theorem = AB² = OA² + OB²

= 14² +14²

Area of sector OAB =

=

Area of triangle AOB =

So area of minor segment – OACB =area of sector – area of triangle

= 154 – 98 = 56cm²

Area of major segment = area of circle - area of minor segment

= 44×14 – 56 = 560cm²