Circle A has a radius of 3 3 and a center of (2 ,4 )(2,4). Circle B has a radius of 2 2 and a center of (4 ,7 )(4,7). If circle B is translated by <2 ,-3 ><2,−3>, does it overlap circle A? If not, what is the minimum distance between points on both circles?
1 Answer
Explanation:
What we have to do here is
color(blue)"compare "compare the distance (d) between the centres of the circles to thecolor(blue)"sum of the radii"sum of the radii
• " if sum of radii">d" then circles overlap"∙ if sum of radii>d then circles overlap
• " if sum of radii"< d" then no overlap"∙ if sum of radii<d then no overlap
"before calculating d we require to find the 'new' "before calculating d we require to find the 'new'
"centre of B under the given translation which does"centre of B under the given translation which does
"not change the shape of the circle only it's position"not change the shape of the circle only it's position
"under a translation "((2),(-3))
(4,7)to(4+2,7-3)to(6,4)larrcolor(red)" new centre of B"
"since the centres have the same y-coordinate then"
"d is the difference in the x-coordinates"
rArrd=6-2=4
"sum of radii "=3+2=5
"since sum of radii">d" then circles overlap"
graph{((x-2)^2+(y-4)^2-9)((x-6)^2+(y-4)^2-4)=0 [-10, 10, -5, 5]}
