1.

Consider P,Q,R to be vertices with integral coordinates and (|PR|+|RQ|)^(2)lt8. Area (/_\PQR)+1 then

Answer»

`/_R` can be a right angle
`/_\PQR`can be isosceles
`P,Q,R` can lie on a square
`P,Q,R` can lie on circle centred on MIDPOINT of line segment `PQ`

Solution :`|PR|^(2)+|RQ|^(2)ge2|PR||RQ|`
`|PR|.|RQ|ge 2Ar(/_\PQR)`
`implies8Ar(/_\PQR)le|PR|^(2)+|RQ|^(2)+4aR(/_\PQR)`
`le|PR|^(2)+|RQ|^(2)+2.|PR|^(2).|RQ|lt8Ar(/_\PQR)+1`
`implies8Ar(/_\PQR)=|PQ|^(2)+|QR|^(2)+4Ar(/_\PQR)` and
`|PQ|^(2)+|QR|^(2)=2|PQ|.|QR|=4Ar(/_\PQR)`
`:./_R=9^(@)` and `RP=RQ`


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