A chord of a circle of radius 10 cm subtends a right angle at the centre Find the area of the corres...

Question

A chord of a circle of radius 10 cm subtends a right angle at the centre Find the area of the corresponding minor segment

Accepted Answer

Here AB be the chord which is subtending an angle 90° at the center O.

It is given that the radius (r) of the circle = 10 cm

Area of minor sector = (90/360°)×πr²

= (¼)×(22/7)×10²

Or, Area of minor sector = 78.5 cm²

Also, area of ΔAOB = ½×OB×OA

Here, OB and OA are the radii of the circle i.e. = 10 cm

So, area of ΔAOB = ½×10×10

= 50 cm²

Now, area of minor segment = area of minor sector – area of ΔAOB

= 78.5 – 50

= 28.5 cm²

NCERT Solutions Class 10 Mathematics Solutions for Areas Related to Circles - Exercise 12.2 in Chapter 12 - Areas Related to Circles