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SAT® Math

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Pizza Delivery Circles

SATMAT-OF4NLE

J's Pizza offers delivery to anyone living up to R miles away from their restaurant. K's Pizza offers delivery, also, but they only will deliver to people living up to $ \frac { 1 }{ 2 } R $ miles away from their restaurant. The circles which outline the areas to which each of these two restaurants will deliver do not overlap, but they are tangent to each other.

Adam feels fortunate because he lives at the point of tangency, and thus, he can receive delivery from either restaurant. If Adam lives at the origin on a coordinate map, and if J's pizza is located at $(-12,-5)$ on the same coordinate map; then, which of the following is an equation for the circle outlining delivery coverage for K's pizza on this coordinate map? (Calculator)

A

$ { (x+6) }^{ 2 }+{ (y+2.5) }^{ 2 }=6.5 $

B

$ { (x-6) }^{ 2 }+{ (y-2.5) }^{ 2 }=6.5 $

C

$ { (x-6) }^{ 2 }+{ (y-2.5) }^{ 2 }=42.25 $

D

$ { (x+6) }^{ 2 }+{ (y+2.5) }^{ 2 }=42.25 $