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

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Answer 1 · 2018-02-09T10:02:30

Circles A and B overlap.

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Circle A - $C e n t e r O_{A} (5, 3), R_{A} = 4$ $Center O_A (5,3), R_A = 4$

Circle A - $C e n t e r O_{A} (1, 4), R_{A} = 3$ $Center O_A (1,4), R_A = 3$

Circle B translated by (2,4)

New center of B $O_B ((1+2),(4+4)) => ((3),(8))$

$vec(O_A O_B) = sqrt((5-3)^2 + (3-8)^2) = sqrt29 ~~ 5.39$

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

Since $R_A + R_B > vec(O_A O_B)$ , circles A and B overlap.

Circle A has a radius of 4 44 and a center of (5 ,3 )(5,3)(5 ,3 ). Circle B has a radius of 3 33 and a center of (1 ,4 )(1,4)(1 ,4 ). If circle B is translated by <2 ,4 ><2,4><2 ,4 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?