Circle A has a center at #(5 ,4 )# and an area of #16 pi#. Circle B has a center at #(12 ,8 )# and an area of #9 pi#. Do the circles overlap? If not, what is the shortest distance between them?

1 Answer
May 3, 2018

they don't over lap
the shortest distance between them is #sqrt(65) - 7 ~~# 1.062257748

Explanation:

area of Circle A = #pi*# #(Ra)^2#
16#pi# = #pi * Ra^2#
#Ra^2# = 16
Ra = 4

area of Circle B = #pi* Rb^2#
#9 pi# = #pi * Rb^2#
9 = #Rb^2#
Rb = 3

the distance between the center points is:
#sqrt((delta x)^2 + (delta y)^2)#
#delta x# = Xa - Xb = 5 - 12 = -7
#delta y# = Ya - Yb = 4 - 8 = -4
#sqrt((-7)^2 + (-4)^2)# = #sqrt(65)# #~~# 8.062257748

#because# Ra + Rb < #sqrt((delta x)^2 + (delta y)^2)#
#therefore# they didn't overlap.

the shortest distance between them is:
Gap = Distance between 2 center points - Ra - Rb
= #sqrt(65)# - 4 -3
#~~# 1.062257748

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