Question

a chord is 10 cm long is drawn in a circle whose radius is 5√3cm.find the area of both the segments

Answer 1

Let AB = chord  

O = centre of circle  

x = 1/2 angle subtended at centre  

Then  

sin(x) = 5/5sqrt(2)  

= 1/sqrt(2)  

x = pi/4  

Angle subtended = 2x  

= pi/2  

Area of sector AOB = r^2(2x)/2  

= (5sqrt(2))^2 * (pi/2) /2  

= 50pi/4  

Area of triangle AOB = 1/2*(5sqrt(2))^2sin(pi/2)  

= 1/2 * 50  

= 25  

Area of minor segment = 50pi/4 - 25  

= 39.27 - 25  

= 14.27  

Area of major segment = pir^2 - 14.27  

= 157.08 - 14.27  

= 142.81

Answer 2

Answer:

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