In a circle of radius 21cm, an arc subtends an angle 60 degree at the centre Find (i) - Maths - Coordinate Geometry

Question

In a circle of radius 21cm, an
arc subtends an angle 60 degree at the centre Find

(i) 
the length of the arc (ii) area of the sector formed by
the arc 
(iii)area of the line segment
formed by the corresponding chord

Gursheen kaur. · Accepted Answer

Radius (r) of circle = 21 cm

Angle subtended by the given arc = 60°

Length of an arc of a sector of angle θ = $\frac{θ}{360^{0}} \times 2 π r$

Length of arc ACB = $\frac{60^{0}}{360^{0}} \times 2 \times \frac{22}{7} \times 21$

$= \frac{1}{6} \times 2 \times 22 \times 3$

= 22 cm

Area of sector OACB = $\frac{θ}{360^{0}} \times π r^{2}$

$= \frac{60^{0}}{360^{0}} \times \frac{22}{7} \times {(21)}^{2} = \frac{1}{6} \times \frac{22}{7} \times 21 \times 21 = \frac{1}{2} \times 22 \times 3 \times 7 = 11 \times 3 \times 7 = 231 {c m}^{2}$

In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠OAB + ∠AOB + ∠OBA = 180°

2∠OAB + 60° = 180°

∠OAB = 60°

∴ ΔOAB is an equilateral triangle.

Area of ΔOAB = $\frac{\sqrt{3}}{4} \times {(s i d e)}^{2}$

$= \frac{\sqrt{3}}{4} \times {(21)}^{2} = \frac{441 \sqrt{3}}{4} {c m}^{2}$

Area of segment ACB = Area of sector OACB − Area of ΔOAB

$= (231 - \frac{441 \sqrt{3}}{4}) {c m}^{2}$

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In a circle of radius 21cm, an arc subtends an angle 60 degree at the centre. Find (i) the length of the arc (ii) area of the sector formed by the arc (iii)area of the line segment formed by the corresponding chord.

In a circle of radius 21cm, an arc subtends an angle 60 degree at the centre. Find

(i) the length of the arc (ii) area of the sector formed by the arc

(iii)area of the line segment formed by the corresponding chord.