Circle A has a radius of $3$ and a center of $(5 ,9 )$ . Circle B has a radius of $4$ and a center of $(1 ,2 )$ . If circle B is translated by $<3 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T10:43:41

$R_A + R_B$ $color(green)((7))$ $>$ $vec(O_AO_B)$ $color(blue)((4.123))$ , the two circles A & B overlap.

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Circle A $O_A (5,9), R_A = 3$ , Circle B $O_B (1,2), R_B = 4$

$O_B$ $translated$ $by$ $(3,2)$

New $O_B = ((1+3),(2+3)) => ((4),(5))$

Distance $vec(O_AO_B) = sqrt((4-5)^2 + (5-9)^2) = sqrt17 ~~ 4.123$

Sum of radii $R_A + R_B = 3 + 4 = 7$

Since $R_A + R_B$ $color(green)((7))$ $>$ $vec(O_AO_B)$ $color(blue)((4.123))$ , the two circles A & B overlap.

Circle A has a radius of 3 3 and a center of (5 ,9 )(5 ,9 ). Circle B has a radius of 4 4 and a center of (1 ,2 )(1 ,2 ). If circle B is translated by <3 ,2 ><3 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?