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+clc,clear

+//Example 4.13

+//To determine area of intersection of 2 circles

+

+d=7 //distance between centres in cm

+r1= 5 //radius of first circle in cm

+r2= 4 //radius of second circle in cm

+

+//use  law of cosines

+cos_alpha=(d^2+ r1^2 - r2^2 ) /(2*d*r1)

+cos_beeta=(d^2+ r2^2 - r1^2 ) /(2*d*r2)

+

+//from the geometry of the figure 

+//all the angles below are in radians

+alpha= acos(cos_alpha)

+beeta= acos(cos_beeta)

+angle_BAC = alpha

+angle_ABC = beeta

+angle_CAD =2* angle_BAC

+angle_CBD =2* angle_ABC

+

+//required area = area at segment CD in circle at A and at B

+area_K = r1^2*(angle_CAD-sin(angle_CAD))/2   + r2^2*(angle_CBD-sin(angle_CBD))/2   

+printf('Area of intersection of 2 circles = %.2f cm^2',area_K)