Circle A has a radius of $1$ $1$ and a center of $(2, 4)$ $(2 ,4 )$ . Circle B has a radius of $2$ $2$ and a center of $(4, 5)$ $(4 ,5 )$ . If circle B is translated by $< 1, 4 >$ $<1 ,4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T12:06:11

Two circles DO NOT OVERLAP

Minimum distance between both circles $= 5.83 - 3 = 2.83$ $= 5.83 - 3 = color(brown)(2.83$

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$O_A ((2),(4)), R_A = 1, O_B ((4),(5)), R_B = 2$

Circle B translated by $((1),(4))$

Sum of Radii $R_A + R_B = 1 + 2 = color(green)(3$

New coordinates of $O_B = ((4+1),(5+4)) => ((5),(9))$

Distance d = $vec(O_AO_B) = sqrt((5-2)^2 + (9-4)^2) = sqrt34 ~~ color(blue)(5.83$

$R_a + R_B < vec(O_AO_B)$ . Hence the Two circles DO NOT OVERLAP

Minimum distance between both circles $= 5.83 - 3 = color(brown)(2.83$

Circle A has a radius of 1 11 and a center of (2 ,4 )(2,4)(2 ,4 ). Circle B has a radius of 2 22 and a center of (4 ,5 )(4,5)(4 ,5 ). If circle B is translated by <1 ,4 ><1,4><1 ,4 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?