#"what we have to do here is compare the distance (d)"#
#"between the centres to the sum/difference of the radii"#
#• " if difference of radii">d" then one circle inside other"#
#• " if sum of radii">d" then circles overlap"#
#• " if sum of radii"< d" then no overlap"#
#(x-1)^2+(y-7)^2=25," centre"=(1,7), r=5#
#(x+3)^2+(y+3)^2=9," centre "=(-3,-3),r=3#
#"to calculate d use the "color(blue)"distance formula"#
#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#"let "(x_1,y_1)=(1,7)" and "(x_2,y_2)=(-3,-3)#
#d=sqrt((-3-1)^2+(-3-7)^2)#
#color(white)(d)=sqrt(16+100)=sqrt116~~10.77#
#"difference of radii "=5-3=2#
#"sum of radii "=5+3=8#
#"since sum of radii"< d" then no overlap"#
#"maximum distance "=d+" sum of radii"#
#color(white)(xxxxxxxxxxxxxx)=10.77+8=18.77#
graph{((x-1)^2+(y-7)^2-25)((x+3)^2+(y+3)^2-9)=0 [-20, 20, -10, 10]}
