Question

O is the centre of a circle of radius 5 cm. The chord AB subtends an angle of 60° at the centre. Then the area of the circle not included in the triangle AOB is approximately equal to​

Answer 1

Answer:

76cm2

Step-by-step explanation:

Area or circle=

$\pi \: {r}^{2}$

=78.5

Area of Aob= 1/2 r2

= 2.5

Area of remaining portion = 78.5-2.5=76

Answer 2

The area of the circle not included in the triangle AOB is 67.68 cm².

Given:

Radius of the circle = 5 cm

Angle subtended by the chord = 60°

To Find:

Area of the circle not included in the triangle AOB

Solution:

In triangle AOB,

∠AOB = 60°

and since AO = BO = 5 cm (radius of the circle)

⇒ ∠OAB = ∠OBA

and ∠OAB + ∠OBA + ∠AOB = 180

2∠OAB = 120

⇒ ∠OAB = ∠OBA = 60

Thus, triangle AOB is an equilateral triangle.

AB = 5 cm

Area of the triangle AOB = √3/4 × 5 × 5

= 25√3/4

Area of the circle = π × 5 × 5

= 25π

Area of the circle not included in triangle AOB = 25π - 25√3/4

= 78.5 - 10.82

= 67.68 cm²

Thus, the area of the circle not included in the triangle AOB is 67.68 cm².

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