Circle A has a center at $(2, 8)$ $(2 ,8 )$ and a radius of $4$ $4$ . Circle B has a center at $(- 3, 3)$ $(-3 ,3 )$ and a radius of $3$ $3$ . Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2016-04-04T01:57:57

Circles do not overlap. Smallest distance $d_{b} = 5 \sqrt{2} - 7 = 0.071067$ $d_b=5sqrt2-7=0.071067" "$ unit

Compute the distance $d$ $d$ between centers using distance formula

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$d = \sqrt{{(2 - - 3)}^{2} + {(8 - 3)}^{2}}$ $d=sqrt((2--3)^2+(8-3)^2)$

$d = 5 \sqrt{2}$ $d=5sqrt2$

Add the measurements of the radii

$r_{t} = r_{1} + r_{2} = 4 + 3 = 7$ $r_t=r_1+r_2=4+3=7$

Distance $d_{b}$ $d_b$ between circles

$d_{b} = d - r_{t} = 5 \sqrt{2} - 7 = 0.071067$ $d_b=d-r_t=5sqrt2-7=0.071067" "$

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God bless...I hope the explanation is useful.

Circle A has a center at (2 ,8 )(2,8)(2 ,8 ) and a radius of 4 44 . Circle B has a center at (-3 ,3 )(−3,3)(-3 ,3 ) and a radius of 3 33 . Do the circles overlap? If not, what is the smallest distance between them?