Question Number 23131 by ajfour last updated on 26/Oct/17
Commented by ajfour last updated on 26/Oct/17
$${Q}.\mathrm{23122}\:\:\:\:\left({B}\right)\:{pentagonal} \\ $$
Commented by math solver last updated on 26/Oct/17
$$\:\mathrm{i}\:\mathrm{think}\:\mathrm{answer}\:\mathrm{can}\:\mathrm{also}\:\mathrm{be}\:\mathrm{circular}\: \\ $$$$\mathrm{region}\:... \\ $$$$\mathrm{in}\:\mathrm{q}.\:\mathrm{it}\:\mathrm{is}\:\mathrm{said}\:\mathrm{points}\:\mathrm{P}_{\mathrm{i}} \:\mathrm{are}\:\mathrm{on}\: \\ $$$$\mathrm{circumference}\:\:\mathrm{of}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{R}=\mathrm{1}. \\ $$$$\mathrm{so}\:\mathrm{let}'\mathrm{s}\:\mathrm{make}\:\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\: \\ $$$$\mathrm{say}\:\mathrm{r}=\mathrm{0}.\mathrm{25}\:\mathrm{so}\:\mathrm{all}\:\mathrm{the}\:\mathrm{points}\:\mathrm{in} \\ $$$$\mathrm{circular}\:\mathrm{region}\:\mathrm{will}\:\mathrm{definitely}\:\mathrm{be}\: \\ $$$$\mathrm{closer}\:\mathrm{to}\:\mathrm{O}\:\mathrm{than}\:\mathrm{P}_{\mathrm{i}} .\: \\ $$
Commented by math solver last updated on 26/Oct/17
$$\mathrm{sir}\:\mathrm{plz}\:\mathrm{do}\:\mathrm{tell}\:\mathrm{where}\:\mathrm{i}\:\mathrm{m}\:\mathrm{wrong} \\ $$
Commented by ajfour last updated on 26/Oct/17
$${the}\:{boundary}\:{of}\:{the}\:{area}\:{will}\:{be} \\ $$$${the}\:{points}\:{that}\:{are}\:{equidistant} \\ $$$${from}\:{the}\:{centre}\:{O}\:{and}\:{the} \\ $$$${nearest}\:{point}\:{among}\:{P}_{\mathrm{1}} ,{P}_{\mathrm{2}} ,{P}_{\mathrm{3}} ,{P}_{\mathrm{4}} , \\ $$$${and}\:{P}_{\mathrm{5}} . \\ $$
Commented by math solver last updated on 26/Oct/17
$$?\:\mathrm{what}\:\mathrm{you}\:\mathrm{mean}? \\ $$$$\mathrm{can}'\mathrm{t}\:\mathrm{be}\:\mathrm{answer}\:\mathrm{circular}\:\mathrm{region} \\ $$
Commented by ajfour last updated on 26/Oct/17
$${consider}\:{pentagon}\:{divided}\:{into} \\ $$$$\mathrm{5}\:{triangles}\:{with}\:{common}\:{vertex} \\ $$$${O}.\:{In}\:{any}\:{one}\:{triangle}\:{the} \\ $$$${boundary}\:{of}\:{the}\:{required}\:{region} \\ $$$${is}\:{the}\:{set}\:{of}\:{points}\:{equidistant} \\ $$$${from}\:{O}\:{and}\:{as}\:{well}\:{as}\:{one}\:{of} \\ $$$${the}\:{other}\:{two}\:{vertices}\:{that}\:{is} \\ $$$${nearer}\:{to}\:{tbe}\:{boundary}\:{locus}\:{point}. \\ $$$${Not}\:{circular}.\:{It}\:{is}\:{the}\:{region} \\ $$$${witbin}\:{the}\:{pentagon}\:{formed}\:{by} \\ $$$${the}\:{perpendicular}\:{bisectors}\:{of} \\ $$$${OP}_{\mathrm{1}} ,\:{OP}_{\mathrm{2}} ,\:...,\:{OP}_{\mathrm{5}} \:. \\ $$
Commented by math solver last updated on 26/Oct/17
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:! \\ $$