"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]}
