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Question Number 182429 by mr W last updated on 09/Dec/22

Commented by mr W last updated on 09/Dec/22

two circles with radius r have a  distance of 3r from center to center.  two points are randomly selected   inside the circles.  1) what is the average distance   between both points?  2) what is the probability that the  distance between both points is less  than 3r?

$${two}\:{circles}\:{with}\:{radius}\:{r}\:{have}\:{a} \\ $$$${distance}\:{of}\:\mathrm{3}{r}\:{from}\:{center}\:{to}\:{center}. \\ $$$${two}\:{points}\:{are}\:{randomly}\:{selected}\: \\ $$$${inside}\:{the}\:{circles}. \\ $$$$\left.\mathrm{1}\right)\:{what}\:{is}\:{the}\:{average}\:{distance}\: \\ $$$${between}\:{both}\:{points}? \\ $$$$\left.\mathrm{2}\right)\:{what}\:{is}\:{the}\:{probability}\:{that}\:{the} \\ $$$${distance}\:{between}\:{both}\:{points}\:{is}\:{less} \\ $$$${than}\:\mathrm{3}{r}? \\ $$

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