In a circle of radius 14 cm, an arc subtends an angle of $120^\circ$ at the centre. If sqrt(3) = 1.73 then the area of the segment of the circle is

Question

KollegeApply · Accepted Answer

Radius of the circle, r = 14 cm Draw a perpendicular OD to chord AB. It will bisect AB. $\angle$A = 180 - ($90^\circ$ + $60^\circ$) = $30^\circ$ "cos" 30^circ = "AD"/"OA" =>sqrt(3)/2 = "AD"/14 =>"AD" = 7sqrt(3) `=> "AB" = 2xx"AD"=14sqrt(3) "cm" "sin" 30^circ = "OD"/14 => $\frac{1}{2}$ = "OD"/14` $\Rightarrow$ OD = 7 cm Area of minor segment = Area of sector OAPB − Area of triangle AOB `=theta/360^circpi("OA")^2-$\frac{1}{2}$xx"OD"xx"AB" =120^circ/360^circxx22/7(14)^2- $\frac{1}{2}$xx7xx14sqrt(3)` =205.33 - 84.77 = 120.56 cm2 Hence, the correct answer is option (a). [Solution diagram: 77503_solution_1.png]

AChoose Your Answer