Question

A chord subtends an anle of 9°at the centre of a circle who chord is 20 cm. Compute the area of the correspoding major segmen of the circle.​

Answer 1

$\huge\underline\mathrm{Question}:-$

A chord subtends an angle of 90°at the centre of a circle whose chord is 20 cm. Compute the area of the corresponding major segment of the circle.

$\huge\underline\mathrm{SoluTion}:-$

Point to note:

Area of the sector = θ/360 × π × r²

Base and height of the triangle formed will be = radius of the circle

Area of the minor segment = area of the sector – area of the triangle formed

Area of the major segment = area of the circle – area of the minor segment

Now,

Radius of circle = r = 20 cm and

Angle subtended = θ = 90°

Area of the sector = θ/360 × π × r² = 90/360 × 22/7 × 202

Or, Area of the sector = 314.2 cm2

Area of the triangle = ½ × base × height

= ½ × 20 × 20 = 200 cm²

Area of the minor segment = 314.2 – 200 = 114.2 cm²

Area of the circle = π × r²

Area of the major segment = π × r² – 114.2 = 1142 .94 cm².

So, the area of the corresponding major segment of the circle = 1142 .94 cm²