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Question Number 118308 by otchereabdullai@gmail.com last updated on 16/Oct/20

Commented by otchereabdullai@gmail.com last updated on 16/Oct/20

please help

$$\mathrm{please}\:\mathrm{help}\: \\ $$

Answered by 1549442205PVT last updated on 16/Oct/20

Commented by 1549442205PVT last updated on 16/Oct/20

The positon of the market satisfying requirement of the problem need must lying on the midline of MN and the the circle with the center at P and radius R=10 km.Hence,the market is the intersection point of the midline d of MN and the circle (P,10km).Since d∩(P)={I,H},so we get two position of the market satisfying the problem The most convenient is the point I since IM+IN+IP<HM+HN+HP

$$\mathrm{The}\:\mathrm{positon}\:\mathrm{of}\:\mathrm{the}\:\mathrm{market}\:\mathrm{satisfying} \\ $$$$\mathrm{requirement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{need}\:\mathrm{must} \\ $$$$\mathrm{lying}\:\mathrm{on}\:\mathrm{the}\:\mathrm{midline}\:\mathrm{of}\:\mathrm{MN}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{the}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{the}\:\mathrm{center}\:\mathrm{at}\:\mathrm{P}\:\mathrm{and}\:\mathrm{radius}\: \\ $$$$\mathrm{R}=\mathrm{10}\:\mathrm{km}.\mathrm{Hence},\mathrm{the}\:\mathrm{market}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{intersection}\:\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{midline}\:\mathrm{d}\:\mathrm{of} \\ $$$$\mathrm{MN}\:\mathrm{and}\:\mathrm{the}\:\mathrm{circle}\:\left(\mathrm{P},\mathrm{10km}\right).\mathrm{Since}\: \\ $$$$\mathrm{d}\cap\left(\mathrm{P}\right)=\left\{\mathrm{I},\mathrm{H}\right\},\mathrm{so}\:\mathrm{we}\:\mathrm{get}\:\mathrm{two}\:\mathrm{position} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{market}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{problem} \\ $$$$\mathrm{The}\:\mathrm{most}\:\mathrm{convenient}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point}\:\mathrm{I} \\ $$$$\mathrm{since}\:\mathrm{IM}+\mathrm{IN}+\mathrm{IP}<\mathrm{HM}+\mathrm{HN}+\mathrm{HP} \\ $$

Commented by otchereabdullai@gmail.com last updated on 16/Oct/20

Am much much greatful for ur time sir may God bless you

$$\mathrm{Am}\:\mathrm{much}\:\mathrm{much}\:\mathrm{greatful}\:\mathrm{for}\:\mathrm{ur}\:\mathrm{time}\: \\ $$$$\mathrm{sir}\:\mathrm{may}\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you} \\ $$

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